My 2003 AF 1150 states not to occupy or store the camper without the floor being supported by 3, 5" minimum wide supports. It doesn't say anything about the tanks, other than being careful not to fill too fast or overfill which can swell the tank enough to cause damage....regardless if supported or not.
It's possible that these "issues" were remedied in the new aluminum frames. Mine is wood, last year I believe for the wood frames. I don't ever take mine off the truck when camping, and I always store it on timbers. 12 years and no damage so far. Well....at least not that kind of damage. I did back into it once.