This was brought up kind of as a joke somewhere else, but I was wondering if the rules address this.

Do you have any special rights as the owner of a figure that is friendly to your opponent's force.

If I go to a tournament and my opponent switches figures with Copycat and then proceeds to do something that I think could damage my figure (like eating cheetoes, or holding the figure when turning the dial) do I have any rights? This would also apply to mind controlled figures.

Is it written anywhere that only the owners of figures can move or click them? Or can you tell your opponent that you will do all the moving and clicking at their direction. What happens if they don't listen or damage your figure, can you get a judge involved?

I think here it comes down to simple etiquette and being responsible/respectful.

If you own the physical piece, you have all the rights of ownership to that piece. If you don't want your opponent touching your piece, you have all the right to stop them from touching it. But this could be considered poor sportsmanship/etiquette.

Yeah...it'd be like playing against a slightly more neurotic version of Woody Allen.

"Yeah, yeah...so see...that's my figure. My figure. MY FIGURE! So...yeah....uhh, y'know so touching it is like a VIOLATION of of of...you know...life and stuff so OH MY GOD YOU'RE TURNING THE DIAL! Aaiaiaiaiaiaiaiaia!!!!!"

If you do not want your opponent touching your figures, offer to move it for them.

I would just ask that they stare deep into my eyes while they touch my piece and turn it ever gently and slowly.

This is going to cause an upswing in table flipping nerd rage. Story at 11.

IMO, if you are choosing to use the game piece in a game, you are giving implied consent for your opponent in the case of something like Copycat, or even Mind Control. If you are bringing your piece to a public place, any number of random things, while unlikely, may befall said piece. (Provided a reasonable amount of care)

Personally, when I use Mind Control, and it is just a single action, I let the owner do all the moving and clicking.

When I use copycat, I will want to move the piece myself. Now my own personal politeness would allow the owner to click the damage if they prefer, but the figure at that point in the game, is under MY control. I should be able to click the damage on a figure under my control if I want to.

So to sum up: (again this is just my opinion on the matter in lieu of any actual hard rules)

1. IF you don't want anything to happen to a piece, don't bring it.
2. If you do want to limit your opponent's contact with some treasured piece, be as polite as possible, and ask as nicely as possible. Also be willing to accept no as an answer, or if that is not acceptable, be prepared for the consequences of that decision. (Potential forfeit/DQ)

I don't mind my opponent holding my ASM Man-Thing if it helps. What? Someone had to say that.

with a single letter change I can actually make this much much dirtier, but I don't wanna get booted so you'll all have to use imagination

I don't know where this implied consent came from.
My figures, my team.
It's only in the latest sets that we have had anything (aside from one time attacks with mind control), that allow a player to fully take control of your pieces.
I don't think many people who paid for their pieces signed up for a game that allows anyone they play against to just snatch up their pieces and use them willy nilly because a card now says they can.
Personally, I'm not neurotic about it, so I don't really care as long as the other player isn't being careless with my stuff. (Like it was said earlier, it's an etiquette issue).
But you aren't in control of how the other person acts with your stuff and you have no idea who you are going to play against each round and how they will treat your property.
I can see this being a very touchy subject for some, especially IF we start hearing stories about careless players who break other players pieces and refuse to cover the damages.

That's incorrect. In 2007, Deadman from the Justice League set got his possession power that let him take control of a character until he or the possessed character was ko'd or he voluntarily ended the possession.

Both in terms of time and number of pieces released, that was closer to the beginning of the game than it is to now, so it doesn't qualify as one of the latest sets by any reasonable means.

I think its fine to allow the owner of the piece to do the moving/clicking. If it becomes an issue, call the judge.

I knew someone would correct me with Deadman after I posted.
I just don't look at him in the same way, maybe because it was so hard to pull off.
But regardless this new situation doesn't even require an attack roll and we haven't seen a power like that since Deadman (and maybe Jericho) so people aren't used to it (especially newer players).

Back to the actual intent of my original post, there isn't an implied consent.
I bet if we talked to any number of players they'd say that all they agreed to when playing at the tournament was playing their own figures unless specifically asked by another player to borrow something.
Again, I don't care, I like the switcharoo scenarios, and build your worst team and switch scenarios, but I can't tell another player they're wrong for not wanting to allow others to play their figures. Some people have quirks like that and I'm sure when they started playing this game they didn't expect this type of situation to arise in play.