Hi Todd,
A couple years ago I rented a Ford Expedition from Enterprise. They handled the insurance and all the paperwork.
We were stopped at the US side and the guy asked if it was my vehicle. I said no, it was a rental and asked if he wanted
to see tha paperwork. He said no and waived us on through. Got the green light at the Mexico side and never had a
problem the whole time. It worked out well, but it wasn't cheap.
From my experience it was not a problem at all. I know some others have done that too. Have a great time.