In my old age, I'm looking more to 3rd Party opinions rather than the old 'he said -> she said' stuff. Or, as I like to say, 'I'm right; just ask me'!
I 'thought' I'd understood prior that any RV Chassis should be Earth grounded, especially while on AC operation. So, I chased it down a little on line. From this lengthy Thread comes this point in Post #3:
RV Grounding vs. Residential Grounding
An RV 'shore' power plug should act like an auxilary breaker box. Neutral should not be grounded to RV chassis. RV chassis should be connected to shore power ground connection. Question to ask yourself is when you step off the step off the RV with a hand on the RV metal chassis will the RV chassis be at the same potential as the ground being stepped on. The best way to ensure this is use the shore power ground.
In the case of any short to RV Chassis causing the Chassis to be hot, you want it to be Earth grounded, just like any 'Old School' Saw or Drill or House Fridge Chassis, etc.. Today, Tools are double-insulated, of course, due in part to bad or broken Grounds at Construction Sites. One fine point is supposedly that you never want to have an Outlet 'appear' to have an Earth Ground, by the 3rd pin presence, when it doesn't.
In any number of weird scenarios, like something electrically 'hot' falling against a metal-skinned Trailer or the Chassis, you never want a scenario where those surfaces could go 'hot' and your Body is the only path to Ground. A grounded RV of any size wouldn't affect the Battery either way, unless someone can chime in with an interesting scenario...
Part of the whole safety 'thing' is to use a GFI Outlet first in any TD/TT/CT AC Circuit 'chain', and wire subsequent Outlets to also be GFI'ed. It's my understanding that if you touch a hot RV Chassis w/a bad Earth Ground with GFI'ed Outlets, the GFI will sense the 'goes inta' vs. 'goes outta' current unbalance as current diverts through your Body. It will trip and shut off power.
On not using the Chassis as DC current path return, what Gus said 2x. Mentally, I completely separate the 2 DC concepts. 1) Mechanical - a Chassis mechanically supports 'stuff'. 2) Electrical - a separate 2nd wire completes any/all DC Circuits; not the Chassis. The twain functions never meet... That is, the RV Chassis connects to DC Ground, especially in the case of Chassis Lights, but ideally is not used for 'high' current return paths.