The Catholic canon

Catholic apologists regard the Protestant canon as an Achilles heel of Protestant theology. While the canon is a legitimate issue, that's a two-sided issue. What about the Catholic canon?

What's the basis of the Tridentine canon? Is it evidence? Was the evidence sufficient to favor the Tridentine canon?

But Catholics and Protestants have access to the same evidence. It's not like the Tridentine Fathers had an extra cache of evidence from the secret Vatican archives that tilted the scales in favor of the Tridentine canon. Protestants are looking at the same evidence as Catholics. 

Or is the contention that the evidence is inconclusive, so that must be supplemented by the authority of Rome. The Tridentine canon enjoys a level of certainty that goes beyond the evidence, due to ecclesiastical authority. According to that paradigm, raw ecclesiastical authority is the makeweight which closes the gap between the evidence and certainty.

But in that case, certainty is detached from evidence. In principle, there could be direct certainty with no evidence whatsoever. Certainty by sheer ecclesiastical fiat. Yet Catholic apologists typically argue for the Tridentine canon based on the evidence, as they see it. 

If, on the one hand, evidence is sufficient to settle the canon, then the magisterium is superfluous. If, on the other hand, evidence is insufficient to settle the canon, ecclesiastical authority conjures certainty out of thin air, with nothing corresponding to back it up. That's the dilemma.