It's a little odd running carpet in the kitchen, but I don't see any issue sticking a fridge directly on the carpet. It's perfectly safe. I suppose it's possible to someday give you a bit of grief when the defrost line plugs up, or when you spill a jug of milk....
I'd at least invest in a carpet cleaner machine.... because you will need one.
Bob, back in the 70's they did carpet in the Kitchen & Dining areas in homes. I remember two of our homes having it in there. One was in Ohio. The other here in Springfield, IL.
__________________ Ren: Now listen, Cadet. I've got a job for you. See this button? Ren: Don't touch it! It's the History Eraser button, you fool! Stimpy: So what'll happen? Ren: That's just it. We don't know. Maybe something bad, maybe something good. I guess we'll never know, 'cause you're going to guard it. You won't touch it, will you?