That's wonderful mythology (very Dan Brown-ish) except for the fact that there's zero evidence that Constantine (or any other Roman Emperor) influenced the canon. Constantine's major contribution to Christianity was convening the Council of Nicaea, which - as we discussed above - DID NOT deal with the question of canon. It was concerned with the nature of Christ, and especially the dispute over Arianism. Canon was not an issue. Truthfully, most of the New Testament canon was already widely accepted by Nicaea. Some "decisions" were still to be made, but there was never a "Council" which took a vote and magically declared "these are the 27 books of the New Testament." That was the result of a growing consensus and there's no real date that we can say the New Testament came into being. As I said above, as far as I know it was the Synod of Hippo Regius in North Africa that was the first Christian Council to refer to the 27 books of the New Testament in a way that assumed it was a finished document, but even it didn't declare those 27 books to be the New Testament. It just accepted that they were. And Hippo Regius was after Constantine died. Constantine had little if any influence over the Christian canon, and there's little to no evidence that he cared much about the Christian canon. He was concerned with the christological controversies that were threatening to tear the church apart and given the church's growing influence could have created a major rift in the Empire and he understandably wanted that settled. That was a very different issue from the issue of canon.
The image of an evil Roman Emperor imposing his will on which books were in the New Testament and which were out is quite simply nonsense with no historic foundation. But people keep repeating it as if it happened and most people don't know enough about church history so they swallow it. And, of course, many are suckers for conspiracy theories, especially if they seem to offer reason to call the church and its teachings into question. There are still people who think The Da Vinci Code was real history and either don't realize or won't accept that it's a novel, no more grounded in reality than James Bond.