A few years ago, Shawn from Cav Arms rented an RV from a well known company to attend a machinegun shoot, maybe Knob Creek - can't remember. The RV broke down on the highway and they contacted said company. Company told them to abandon RV, head into town and they'd get another RV. Shawn informed company that they couldn't leave RV as they had restricted class 3 firearms with them. They were instructed to wait.
Cops show up code 3, hold everyone at gunpoint because "weapons were involved" including a young child. It all got sorted out, nothing illegal at all. Employee went off the deep end and called cops because guns were mentioned.
Cav Arms rented the RV in AZ wearing Cav Arms shirts, openly packing sidearms and even told the staff what they were planning.
I don't remember the outcome, but I think the RV company got sued and settled.
I have rented cars and trucks and crossed the country many times with firearms in the last 20 years without a problem. It is not illegal unless it is stated in your contract. Don't be so quick to give up rights and quit.