I think one of the big issues people hit upon with OCs is that there is one single person in charge of the 'canon' and no way for anyone else to fact-check it. I mean, DC comics continuity might be inconsistent, and someone could question the choices the player makes as to what to use and what not to, but at the end of the day, anyone who wants to can look into the canon and see where those choices come from.

Headcanon for canon characters is a trickier subject. I have absolutely seen people who abused it, and people who were taken to task for it. Whether people get called on it or not, I suspect, is largely dependent on how well the character is known and how well the person blends their headcanon into actual canon. If you make good choices, no one minds, but people will call out bad ones.

How often this would actually be an issue vs. the amount of concern people have over the possibility of it happening, I don't really know. I've been in games that had OCs, and my experience with them has been that you could really tell they were OCs. If that had to do with the quality of the players, or the burden of having to develop and keep a character consistent without anything to review, I can't say, but in the end, the issue wasn't so much abuse of the OC concept as it was a lack of creating an engaging character. But I suppose that's a burden the player themselves have to handle.