Othello is even more interesting here. There are no rules excluding a particular move other than "you must capture at least one of your opponents pieces". In that regard its much simpler than chess, and a valid move is more consequential than in Go. Trying to make an illegal move in Othello would be extremely weird.

A reasonable strategy for a computer to play Othello to beat beginners is to literally evaluate the legality of all moves in a predefined order and make the first legal one. The predefined order encodes general positional advantage while the legality check enforces validity.

In short, I strongly agree that making even 1 illegal move in Othello indicates a lack of understanding the rules.