Does Wizards of the Coast really own anything that uses a 20 sided die?

A conversation among a couple of friends brought this question up. My friend states that Wizards of the Coast, who (I believe) came up with the D20 system, can legally claim anything that uses a 20-sided dice as part of their gaming system regardless of whether or not the conversion/game/whatever is meant to be an extension of their product or a completely different game.

I’m not sure this makes any legal sense. I can understand the legalese stating that any fan-made materials can be legally claimed if they use the D20 system, but having WotC claim ownership of anything and everything that uses a 20 sided dice regardless of the game content seems to be quite a stretch. I personally feel like it would be akin to stating “Your movie has vampires in it, therefore Ann Rice owns the copyright”, but I’m no lawyer and I’m not sure if I’m comparing apples to oranges.

In short, can Wizards of the Coast honestly claim copyright over anything that uses a 20 sided dice, regardless of whether or not it’s part of their D20 system?