It's not a question of competence, it's a question of priorities. As long as cheating isn't rampant, there is little reason to spend your time fighting it instead of actually implementing the games.
I don't know anything about the architecture of BGA and BGA's games but I could imagine that your browser would contain information that is supposed to be hidden for you or that it wouldn't check for the legality of a move. If anyone makes illegal moves, they will be caught by the players themselves.
The use of hidden information, that is more annoying because 99%+ of the time, if the opponent does something that seems logical only if he has information he shouldn't, it is either that he played poorly (and got lucky) or took his chance or he is much better at remembering everything that happened and what cards/tiles/... should remain in the deck and deduct hidden information based on open information that you give him credit for or even think possible based on your own limited skills.
If you think someone modded a game, first file a bug report maybe ? Give the table and turn # and explain what is the problem ?
Maybe, before doing that, wait for the game to end and watch it back from their perspective, action per action ?