We live in ours full time and I put down the rubber mats for one simple reason: I'm not an organic chemist.
I'm not really worried about concrete, per se.
More about the gunk on the ground where I park.
Goodyear says that where you store your tires should be clean.
When I pull in to a new space I have no idea what was done before I got there. And it's not like I tote around a pressure washer.
I don't know what types of sealants have been applied or when. Depending on the time of year the same goes for deicers and herbicides / pesticides. And I don't know what that stain is? Maybe the guy's dog peed there or his truck leaked something there?
And I don't know what happens when you mix all that gunk and park my tires on it in the sun?
I figure $30 for peace of mind is cheap.
And then the thing about no weight on the tires / jacking up the vehicle / warping the frame.
Once again: I don't have "authoritative" answers. But, it seems to me like the concern would be the full weight of the vehicle being on one part of the tire for a long time. It seems to me like the stabilizer jacks would help with that. After all, at least some of the load is transferred to them. I'll be able to answer that question more definitively when we pull out of here in a year or two after I heal from the surgery I need.