Yes they do, depending on model. My 9.6 had panels similar to yours, the 10.4 I have now has one large panel further forward giving access to the tanks, and a small one on the side of the box all the way forward through which you can access the shower drain plumbing. The tanks are suspended on nylon webbing.
The concern about filling too fast is the air cannot escape fast enough and the tank will swell, breaking it or its fastenings. This is true of most RVs, not just Bigfoots. It takes only a few psi on the large area of the tank bottom to produce a lot of force.
