The churches burnt one hell of a lot of stuff, but not directly. Instead, this was all done by the explorers and missionaries of the day, on behalf of the church, or by direct/indirect order of the church. I wouldn't have imagined the burning and destruction to be organized at all, because the churches weren't looking for anything. A safer bet would be that said codexes found their way through time, and now sit on the lofty lap of some multibillionare, or even still resting in a temple/ box undeground somewhere. It would be uncharacteristic of the Vatican to hide artefacts away, as doing so would be the equivalent of PR suicide. If it is linked to the Vatican, then the matter would be most likely in the hands of a secret sect, in which case, it wouldn't be in the Vatican Secret Archive
I would love to know more about it. I feel like the web isn´t going to deliver me with any good info on what was done to the codexes. I guess I would have to graduate in history and get me some research funds for this, LOL.
A plausible argument that I read somewhere was about the church gathering and burning/destroying things just because they thought the mayans and aztecs were somewhat religiously linked to heresy, black magic and crap, due to their strange rituals and sacrifices. That is plausible. The hypothesis that they hid it from the world is conspiracy theory, not impossible, but still a big CT, Dan Brown - like .