Who's to say that Council or any other was entirely inerrant and/or infallible?
Themselves?
Others coming after them, not daring to to do anything but validate the proceedings for reason they prefer to (need to?) regard these Councils composed of clearly other than "infallible" men as individuals, all of a sudden become inerrant/infallible when they gather together?
As Christ Himself cited from OT scripture "if a man bears witness of himself he bears false witness".
That's the problem right there.
Not knowing any better (or caring) these particular works were accessed fairly earlier on for passages and verses here and there (AS I ALREADY MENTIONED -- hello?) which in itself does not make those works post el facto into having been Hebrew canon -- thus needing be regarded as truly inspired, even inerrant (inerrant-- not to be confused with "infallible") at the time Christ walked the earth as man.
Saying now as you have "that's all that matters" gives away the game, with that game un-winnable ---unless the writings of the Law and the Prophets Jesus came to fulfill were not known well enough to the very religious authorities He repeatedly upbraided (and CONDEMNED) for not adhering to them, and/or misusing them.