I don't think it makes much of a difference whether 100 people rode a bike once, or one person rode a bike 100 times.
I wouldn't buy a used bike unless I knew what I was doing in terms of being able to make any repairs it would need, and how to inspect a bike to make sure it is a solid ride.
I haven't bought a NEW bike since I was in high school almost 20 years ago, but I worked in bike shops most of my growing up and through college so I feel comfortable with that and always score good deals on rides.
Bikes are pretty darn resilient and last a very long time even without proper maintenance — if it is a shop quality bike vs. a department store Huffy.
By and large rental bikes aren't abused like buying a used mountain bike from someone who actually shreds the singletrack would be. I don't know what the typical client at Golden Triangle is like but whenever I see people on rental bikes they are typically leisure riders, tourists, or people just out for a casual stroll.
I'd assume you would be fine, just make sure to check over everything from the shifting, smoothness of bearings like the bottom bracket and headset, inspect the frame over for dents, bends, or any deformities in the metal, look for things like broken mounting threads etc on the frame that are not repairable and even things like the shape of the tires, brake pads, wheel trueness, etc etc.
Grab the spokes on each wheel and check the spoke tension by feel and see if there are any really loose spokes or anything indicating that the wheel has been beat to crap and brought back to true by throwing the spoke tension completely out of whack (some super tight and some really loose) so the wheel tracks true between the brake pads (you will be snapping spokes in no time as you ride).
If you buy a bike with a front or rear suspension make sure the seals are good, they hold pressure (if an air/oil shock) and the stanchion tubes are not loose.
Check the rear derailleur and hanger alignment by eye and see if there are any signs of it being bent / straightened or weakened in any way as that will render your bike useless if it snaps off and is not replaceable. Look for gouges or scrapes on the rear derailleur that would indicate the bike had been crashed or thrown down to the ground on the drive-side.
I would assume a shop with mechanics selling used bikes would make sure the bikes check out well for liability reasons alone and for their general reputation.
I won't even sell a bike on craigslist without making sure it is fully ready to ride and all dialed in unless I fully indicate that I had not done so in the ad. I would hope that an actual business would go a step or two beyond that.