Where exactly does it quote this on the AOPA US website?
I am a UK citizen (resident alien) living in California and I have renters insurance with no problem and the questions asked at the time the policy was taken out/renewed never even ask for nationality.
My local FBO require Renters Insurance by all pilots and I have never heard of any instance of any problem when it comes to making any claim.
Because you are a resident......
This applies to visiting holiday-maker type pilots whoa re not US based.