Not that it matters because the admins at this site don't seem to care!

It's mostly low rated players who accuse others of cheating, especially in Blitz and Bullet, as they are simply unable to conceive both their own lack of skill and the various levels of advanced players.

You don't typically see this at the top at all, because these people understand what's possible.

None of which invalidates my point .

It absolutely does, because this "extremely commonly held and mistaken belief", as you so eloquently put it, is predominately held by low rated beginners.

I do believe if someone wanted to make a bot that played for them on say Chrome, they could make a bot that analyzed the chess board using a program from the outside that moved the mouse on a Windows level to move the piece. 

But, I don't believe many people, especially those rated 2200 and below, are doing that.

I do agree that the lower rated the player, the more accusations they make about cheaters. But the higher rated, and better a chess player, one becomes, the more silly they will realize it is to think someone rated 1500 (for example) is cheating

Since this discussion has specifically deteriorated into a cheating discussion, locking.

Discussions of cheating, potential cheating or cheat detection are not allowed on the general forums. If you would like to have that discussion, join the following group.

https://www.chess.com/club/cheating-forum

Chess.com takes cheating very seriously:

https://www.chess.com/article/view/chess-com-fair-play-and-cheat-detection

https://support.chess.com/article/648-what-do-i-need-to-know-about-fair-play-on-chess-com

To report a suspected cheater to the Support team, please select Report Abuse under the Help menu, click the report link on the player's profile, or use this link: https://support.chess.com/article/346-contact-us. All reports are investigated, even if there is no immediate visible action.