Not so. First, the Roman Catholic Church accepts as valid all Christian baptisms (even those conducted by non-Christians or atheists!) as long as such baptisms are valid in matter (water) and form (trinitarian) and are done with the intention of doing what the Church does via baptism. As a teenager, I myself was baptized by an Assemblies of God minister, but when my wife and I were reconciled to the Catholic Church our parish priest accepted my baptism as valid. No proof was required; my word of honor alone that it had occurred as described above sufficed.
Second: Only Catholic Christians who are in a state of grace (i.e. those who have been absolved of mortal sin through the Sacrament of Reconciliation*) may sinlessly receive the Body and Blood of our Lord at Communion. Those who come to the altar rail while bearing the stain of mortal sin are unworthy of the Body and Blood of the Lord and are thus guilty of sacrelige if they receive Him; it therefore follows that, since non-Catholics cannot receive absolution via confession and penance, almost all* non-Catholics would be spiritually unworthy of that singular honor.
* Some Christians (Catholic, Protestant, and otherwise) may be absolved of mortal sin by the Holy Spirit via an act of perfect contrition -- but these people are rightly called saints. Such truly holy people are few and far between; therefore, as guardians of the Holy Mysteries of the Eucharist, Catholic priests are obligated to deny Communion to all who have not been absolved of sin through the Sacrament of Reconciliation. In any case, the burden of proof lies with the communicant; priets are under no obligation to ascertain the worthiness of any individual worshiper.