I've never had renter's insurance in the US. I asked insurance guys at their stand at an airshow in 2010. They said they wouldn't cover me as a non-resident legal alien.
I've checked with FBOs that their deductible was about the same as my UK Group expect me to pay, and checked insurance position before renting.
As regards off-airport landings, usually only if you've made a Mayday call. I fly our Group plane into strips in Scotland. The cost to a commercial renter of even a minor mishap in these places makes it very expensive for anyone to rent for this to unknown solo pilots.
But some FBOs offer courses in back-country flying, eg Colorado Flight Centre at Grand Junction.