I would have the letter authorizing you to drive the vehicle. Check with your insurance and their insurance - some companies cover anyone driving the vehicle, others cover only those named in the contract. I would also establish an agreement between me and the RV owner to identify certain responsibilities.
There's an old saying "don't do business with friends or family". I find this to fall into that area. If something goes wrong, it could end up ruining the friendship. A simple "oops, I backed into a post" or "I got a ticket" is easy; but what if something else went wrong. What if the generator/power inverter goes bad? What if the engine block cracks? Things like this aren't so easy to assign blame or determine the root cause, and it could turn into a fight about who's responsible to pay.
While it might be making things more convoluted, RVs can cost big bucks and problems can mean a lot of money at stake - and disagreements about money do ruin friendships.