Do they really check for current registration and insurance on cars for camping?

Yes, they check insurance and registration for both your vehicle and RV. Come prepared! Frankly, that should be a nonissue for folks anyway as you are legally required to have them while driving in CA.

Unfortunately I think they check the sticker but I don't think they call in.

Usually

I don't believe they check them either

That is my understanding, checked at the Kiosk when you arrive

I dont believe they checked

Yes they do