It's certainly open to debate. Most of Paul's churches weren't accepted by the Church in Jerusalem for exactly the reason you listed. I wouldn't call them "original" partly for that reason, and partly because Paul wasn't a first hand witness. I tend to think of them as a set of "first round expansion teams" to use a hockey analogy .
There is some really serious question about the Gospel of John beingn written by an eye witness. Most of the non-conservative theologians I know or have read tend to place it fairly late, say ~85-95, and generally conclude that it wasn't written by the disciple of that name. At least when I studied it, the general agreement was that the Johanine community derived from Paul's churches rather than from John. I'll agree with you on the synoptics, however.
Bookmarks