Freelance CFIs and plane rentals??

I posted a message awhile back about one of my relatives offering me
free flight instruction. He's a very experienced airline pilot and
has done a lot of CFI work in the past. He's still current on his CFI
rating, and the plan is to begin training in June (when I have more
money and he has more time).

Do you think there will be any problem with one of the local FBOs
renting us a plane for my training? Obviously they'll want to check
him out and see his history, but beyond that is there anything I need
to know? Obviously we should just make a couple of calls and see what
their policy is, but I just wanted to know if this was a common
situation or not first. TIA!

Sam