It goes something like:
If you have not already been Baptised, then I Baptise you ...
In Orthodoxy this is something of an issue we are still working out. There are a number of ways which converts can be received, all of which are considered valid when done properly. However, unlike in the RCC where the sacraments have been separated from the church, which is to say that you believe non-Catholics can in certain situations perform "valid" sacraments we don't generally hold to that view. In Orthodox theology (and this is the solid teaching of the fathers both east and west) the grace of the Holy Spirit in the Mysteries flows through the Church. All of the Holy Mysteries (sacraments) are performed in cooperation with the entire Church which is the mystical body of Christ. Thus it is the firm teaching of the Orthodox Church that there are no Mysteries outside off the Church. This is one one of the reasons we don't worry too much about the weird schismatic groups that pop up now and then in both the east and the west. Those who have gravely and obviously separated themselves from the Church can not perform Mysteries since they lack the grace that flows only through the Mystical Body of Christ. The Mysteries to us are not magic. So we are not concerned if someone has the correct matter form and intent, and if at some point 200 years ago they were blessed with what one Roman Catholic theologian referred to as the "Dutch Touch." conferring "valid" apostolic orders.
Now this position has created all kinds of questions specific to the situation in the modern world, some of which we have not thus far worked out with unanimity. Fr. George Florovsky wrote an interesting essay on "The Limits of the Church" in which he noted (IMO correctly) that while we can know with certainty where the Church is (canonical Orthodoxy) and sometimes with a reasonable degree of certainty where it is not (most if not all of the so called Protestant sects) there are gray areas where we just don't know for sure where the exact line is on the other side of which the grace of God necessary for the Mysteries has ceased to flow. Several examples would be the Roman Catholic Church, the non-Chalcedonian Eastern Churches and some of the schismatic Orthodox sects (radical Old Calendarists and the like).
Some jurisdictions have adopted a very narrow interpretation of the rule that the Mysteries do not exist outside the Church and firmly reject any grace in Roman Catholic and all other heterodox sacraments. They typically baptize all converts to Orthodoxy. Others (this is the more moderate position and also by far the more common one in Orthodoxy) are more discerning and will receive converts from other Christian confessions which have performed some form of baptismal ceremony using water, the Trinitarian Formula and whose understanding of baptism is the same as or very close to Orthodoxy's by confession, profession of faith and Holy Chrismation. In the Orthodox Church receiving converts by the Mystery of Chrismation is seen as an act of Oikonomia (a dispensation from a normal discipline for pastoral reasons). It is also accepted that Chrismation can fill with grace that which was empty of it and make whole otherwise defective Mysteries. Thus in the Russian tradition RC priests who convert are not normally re-ordained but are simply vested after Chrismation since the RCC has maintained the outward form of apostolic succession and an Orthodox understanding (generally) of the Holy Mysteries. Even very strict jurisdictions (such as the Russian Church Abroad as opposed to the Moscow Patriarchate) will sometimes receive converts in this manner for unusual reasons. In the Russian Orthodox Church (and here in the OCA) the custom is that Catholics, Oriental Orthodox, and a few of the confessional Trinitarian Protestants (such as Anglicans) are received as converts by Chrismation and are not normally baptized. Non confessional Protestants (so called Evangelicals and the like) are almost always baptized since their baptisms do not even claim to do that which we do. They deny the sacramental nature of baptism. We also baptize when there is any doubt.
Finally it should be noted that we are not quite so legalistic in our approach to double baptism. We also have a conditional formula for baptism but in my experience it is rarely used. (Usually only in cases where an emergency baptism was performed by an Orthodox layman.) Since Mysteries performed outside the canonical boundaries of the Church are presumed to be void and empty of grace, baptism is an acceptable method for receiving all converts. My OCA bishop noted that the custom of receiving converts by Chrismation is an act of Oikonomia and it is never wrong to receive by baptism. Regarding the danger of a double baptism (we also confess "one baptism" in the creed), the Church sees God as rather bigger than the legalistic one that many westerners seem to have embraced. God knows if someone was "validly" (that term is not Orthodox but I will use it for now) baptized before. And they know when we baptize converts we do so out of an abundance of caution. No Orthodox priest is attempting to perform a Mystery that can only be performed once a second time. God understands this and thus no sacrilege is performed.. I have suggested to my priest in the past that we could adopt the use of the conditional formula for some baptisms. He basically asked me "Why? Do you think God doesn't know if someone was already baptized or that we are not attempting to repeat baptism?"
So, cutting to the chase, you avoid "double baptism" either by claiming that nobody can baptise except the Orthodox, or by not baptising converts from the Catholic Church or from Protestant denominations that you recognise as having an (O|o)rthodox view of baptism. The latter is essentially the Catholic approach. The Catholic "conditional baptism" is used with converts from Protestant ecclesial communities with dubious recordkeeping or dubious theology.
He basically asked me "Why? Do you think God doesn't know if someone was already baptized or that we are not attempting to repeat baptism?"
lex orandi, lex credendi ... OF COURSE God knows what's going on. He's God. The point is to make sure WE know what we're doing, and to make explicit what we're doing and what we're not doing. We believe that "double baptism" is a heresy/blasphemy ... so we make sure not to even look like we're doing one. See again the Donatist heresy for historical background.
"God knows if someone was "validly" (that term is not Orthodox but I will use it for now) baptized before. And they know when we baptize converts we do so out of an abundance of caution. No Orthodox priest is attempting to perform a Mystery that can only be performed once a second time. God understands this and thus no sacrilege is performed."
Our parish has had an amazing influx of converts over the past five years and our practice has been as you have outlined. In one instance we baptized someone who most likely had been baptized a Roman Catholic at birth. This was in the case of a young Filipina who had been adoted by some fundamentalist "free church" type Protestants when she was 4 years old. She of course had no baptism records but we did have a paper saying that her birth mother was a Roman Catholic. I communicated with some Jesuits on the island she came from, but they couldn't find any records. Our Metropolitan decided that lacking any concrete evidence that she had been baptized, we needed to baptize her and if we were wrong, he was quite sure God "will understand".
As for marriages, I think we only recognize Roman Catholic marriages as being fully sacramental and require all other converts to "have their marriage blessed" by The Church. I am also aware of several instances where Eastern Rite Catholic priests have converted and their orders are fully recognized (I don;t know about Latin Rite priests though I expect it is the same. We do not accept Anglican ordinations). There is no re-ordination, merely a vesting. I also understand that that caused a problem for at least one such priest while on Mount Athos.
I would like to address the question of the Orthodox view of the validity of Catholic sacraments. The Orthodox hold that the Catholic Church is not validly a part of the Church of Christ and thus (for many Orthodox) is lacking in God' grace. But by what authority can the Orthodox make such a claim. One, if not the chief, charges made by the Orthodox against the Roman church is the rejection of universal jurisdiction by the Roman Pontiff. Within Orthodox ecclessialogy each bishop's jurisdiction, including that of Rome, is limited to his own diocese. By this reasoning, by what authority does the Patriarch of Constantinople, or any of the bishops in the East, have to judge the Bishop of Rome and the Western church? While they may break communion between local churches, how can they issue a judgment of heresy and declare excommunicate from the universal church those who are not under their jurisdiction?