For clarity ... the question was if you would rent it, not swap. Not directed at you per se ... just most of the replies immediately gravitated to swapping, and that was explicitly excluded in the opening post.
I know all of us with good friends and/or swaps to arrange have their opinions, and I too would likely just go for a swap with someone I trust. But let's say you trust the guy in general, he's known on Pinside and you either really want to play one of his pins or vice versa. You neither want to sell, or have a trade offer ... and you're not freely offering to loan out your pins.
Okay, for more clarity, and a real-world example:
I really want an Attack From Mars (among others). I'm largely out of space and not looking to pack more pins in my house for the long-term. Neither am I looking to spend yet more money on pins. So a purchase isn't likely. No one is going to lend me theirs, and I let's say the person really doesn't want to trade for anything I have. Would $100/month be enough to get an AFM owner's interest? I'll gladly pay. Assuming they know that their pin gets very well cared for, is guaranteed that if anything bad happens (roof falls in on it, cat dies inside it, etc..) that I would pay for it in full, etc... So, I know this is very specific, but I think the base need is their. People want to play certain pins, but for whatever reason can't get their hands on one.
Think of it as a step above routing your pins. You get a small financial return and your pin is likely safer, and not likely to get the same amount of play in an arcade...