I would say that in the right circumstances (and hands) this could be a win, win situation. I haven't done anything like this with an aircraft but had an informal arrangement with a boat owner that I'd check on his pride n joy on a regular basis, as well as taking her off the mooring, running the motor, using the winches and airing the sails while he was away on an extended holiday. Worked well, but then I was a regular member of the racing crew and familiar with both owner and vessel. Same with a sports car that I garaged for the owner, I probably put 500km on it in the 6 months that it lived with me, but I made dammed sure that I was on the insurance before I turned the key and to be honest it was a bit of a relief to hand it back intact and without any new stone chips in the paintwork.
BUT - I spend my daylight hours unravelling messes where people assumed (makes an ass of u & me?) that certain factors had been taken care of and ended up with a lot of bent machinery or broken bodies lying around, not to mention scary bills to pay. Make sure that you are both clear on who is doing what and who is responsible. I've known a friendship to come to an end over a $350 4x4 tyre that got cut and needed replacing - what is going to happen if a worn aircraft tyre gets punctured, are you as the pilot looking for free or cheap flying going to pay for the repair/replacement? Your definition of being at fault may differ from the owner's. What about that tank of stale ULP, remember by the time the average aircraft owner is ready to hand over his pride n joy to you, it has probably been sitting around for a good while already and may not be in perfect mechanical condition . Or hypothetically Mr Jabiru owner tosses you the keys and says go for it. What happens when it eats a valve, a through bolt breaks - we all "know" that these things aren't exactly unknown, but even if you land without damage, there is an aircraft to recover and the sticky situation of a motor needing repair. It's not something insurance will cover. Even if it did, excesses on aircraft are often high, who is going to pay that? Don't take it for granted that people are reasonable when the chips are down either - a good friend ended up spending several times the value of a trike that got broken, on legal fees after he came up against someone who was completely pig headed - and wealthy. They eventually agreed to go their own way after 18 months of fighting, but the lawyers still needed paying.
I'm not saying don't do it - far from it, I'd be happy to do it myself, just don't go into it without some thought and discussion, because the cost of getting it wrong could pay for many years of aircraft hire!