I've seen fiberglass roofs crack. I've has a trailer with an aluminum roof and it leaked like a sieve.
Not all rubber roofs are made or installed equally. ORV uses a thicker membrane than others. I drag mine through the trees regularly, and walk on it, and it's never had the slightest bit of damage. My Jayco's roof was quite a bit more delicate...
Also, ORV sands the entire roof structure before installing the membrane, to ensure there's no high spots or burrs that could wear through. And they fully bond it. I wouldn't be worries about it in the slightest.
That said.... covering the trailer or using a UV inhibitor is very good advice. I cover mine whenever it's parked, as it also keeps the rain from being forced through seals and vents when its stormy.