I couldn't imagine ever asking to do that, especially with a brand new camper, it's just WRONG and shows disrespect to you in my opinion. Perhaps a different scenario if you were getting an old camper, but then they should all offer to put in shares towards one if they think they have the right to use it.
Ask them if you can take their 4wd away camping in exchange...it'd be interesting to hear their argument.
Mark.