You know, it never occurred to me to question the authenticity of what we call the Didache beyond the obvious understanding that copyists often made mistakes, though far fewer than translators. The Bible used in the West is a classic example of that.
The Didache we read today is in fact consistent with the quotes from it and principles cited by the Fathers going back at least to St. Irenaeus of Lyon which is a pretty good indication of the accuracy of our copy. At base, though, I suppose we accept it because, like the OT and the NT, The Church does.
I would agree on the parts that are directly attributed to Scripture passages. It's one of the ways we can know we have accurate manuscript copies of Scripture by there being direct quotes taken from the Biblical books throughout the writings of the ECFs. I look at the Didache as probably the work of someone who took notes while hearing the teachings of Jesus and His Apostles before the widespread availability of the written Scripture gathered together in a codice. Some churches may have had all the writings and others only a partial collection. Paul advised that his writings also be read in other local churches and not just the one it may have been addressed to.
There is no denying that the Didache contains things NOT found in Scripture which indicates to me that it may have been a document that was added to over the centuries. With the Bible books, we at least have ALL the manuscript copies written in the original languages, though some are only partially preserved due to the fragile condition of the material they were written on. There are actually THOUSANDS of manuscript copies or partial copies. I don't think that is true with the Didache.
Again, I don't think the Didache has the authority of the inspired Scripture and is why I think it is more of an historical document rather than a doctrinal guide for Christians.