Carfax won't show much if the rental company did the work themselves.

If its a reputable dealer, I wouldn't worry as long as they've inspected it (or it's gone through the certification inspection).

As long as you can verify that it's been inspected, or have it inspected yourself, you should be fine.

The H3 I bought was an ex-loaner out of California, and I didn't hesitate at all.

 

I too bought a "fleet" vehicle. I got mine at a Hummer dealer and got the bumper to bumper Hummer Certified warranty.
I have had no problems - knock on wood - whatsoever. No rattles - no nothing. But I guess even if I do it's covered.
If I were you I'd look into the warrant/certified issue and see what you can get. If you get the warranty or better yet Hummer Certified you're good to go.
Having started my H3 illness by renting one originally in Colorado I can tell you the one I rented was in great shape for having 20k. I also rented one here at home - to help persuade my wife - and it too was solid as a rock.
I think H3's are durable to begin with and rental companies, as stated before, cannot afford to have their cars break down and **** off customers.
Good luck.

 

My brother rented one when he and his 17 year son visited. I would never buy that H3 after the way it was jumped and driven. You heard the expression. "drive it like you rented it"?
PM me as I may be selling my 9000 mile, well driven 2006 H3. It is all stock except 315 BFG MT's. Could sell another set of original 5 285 tires and factory wheels never used if interested. PM me to talk price. It is perfect, absolutely perfect with Adventurers package, factory engine block heater and auto as I ordered it from the factory.Those are the only options I wanted.