Should I be worried ?

You are not being paranoid. My personal experience is that this will just get worse over the years. So much water will eventually pool when the trailer is level, that it will go over the lip and leak into the trailer thru the blower duct. Worst is if all the pooled water freezes. I spent plenty of rainstorms outside de-leveling the trailer or motorhome to drain the roof. And, I've also climbed up on cold mornings to break up ice, because the leak thru the duct becomes even worse when the ice is melting. Your new trailer's roof cannot support the AC and must be re-inforced. The quick fix is as you described with 1/2-3/4 inch plywood, but eventually, that too will sag unless extra cross members are installed. This is not cheap or pretty to do, and this is why the dealer and manufacturer will give you the run around. Document every thing and check the lemon law for new RVs in Texas. You could have a court case. Check with other owners of this trailer. You could have a class action.