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When I fold a hand, I deliberately slide them so that they touch the muck. At that point, my hand is dead and no one can see it

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That really doesn't matter, because the dealer will simply pull them OUT of the muck and show them.

The rule is, if you go all the way THROUGH and INCLUDING showdown, be it if you bet or anyone bets or NOT, if someone demands to see your cards, then anyone at your table can indeed do so (even if they were NOT in the hand).

However, it's really considered BAD form to do this. The rule was created back in the days when cheating was rampant, and thus, when you do this to another player, you are insinuating that they are cheating.

My advice to the OP is this, if no one bets on the river, and you KNOW you don't have the winning hand, and you have someone doing this to you more than once ... MUCK your cards when the dealer comes to you, even if it was checked to you.

That way, you never went all the way to showdown (since you folded when it was your turn, checked or not), and thus they would have NO right to see your cards then.