The real question here does not seem to be how to resign, but how to deal with cheaters. There are ways of dealing with cheaters which are not specific to chess.
After the fact, some might suggest a fistfight, :-) while others might suggest social shaming (i.e., making sure everybody in the club/tournament learns that the person is a cheater). You can also request not to be paired against the cheater in the future. Tournament directors are not required to accommodate your request, but they can consider it. Finally, you can file a formal complaint, although there better be evidence.
Before the fact, you can either be "paranoid" about it (for example, by demanding that the director witness the resignation as someone else suggested), or you can relax and assume good faith knowing that cheating is very rare (unless you play in an environment very different from what I know!). Up to you.
In any case, keeping score is always advisable, for a variety of reasons.
Back to the incident in question: the tournament director has a lot of discretion when dealing with "ambiguous resignations" (ambiguous is how they look to a TD in a "he said, she said" situation). Here's what Tim Just, editor of the USCF rulebook, had to say about it in his book, Just Law:
If an ambiguous resignation is disputed promptly enough, then the game
can simply continue. If the unclear resignation is not discovered
until much later, then the waters get muddy. Some TDs like to award
one point to the player who says they won the game and a half-point to
the player who says they drew the same game—I am not a fan of this
method, but it is widely used. TDs may be able to go over the game
score and adjudicate the result based on the final position. If the TD
cannot determine what happened, they may declare the game a draw or
let the reported score stand. The worst option is for the TD to
declare the game a double forfeit. I cannot recommend that. But
players who get tied up in disputed resignations may want to be
prepared for any of these TD decisions.
(This is all in the context of USCF rules, of course. Your mileage may vary under other jurisdictions.)