not specifically airplanes (I can't loan "mine" out, since I only own 1/40th of it), but I have heartburn about loaning and borrowing. My heartburn stems not from the value of something, but from the potential impact to friendships if something goes wrong. Not from my side, but from "how's my friend going to feel if something happens to ___ while they have it?"
I loaned my RV to a friend a couple of times, and a deer hit him (yeah, deer ran smack into the middle of the coach while said deer was trying to cross the highway in the dark). Cracked a fiberglass skirt and smashed up a wheel cover, so we fixed the crack and pounded out the wheel cover and all was good again. But, I know he felt horrible.
If I borrow something, it WILL get returned in the same or better condition than when borrowed. We borrowed a bunch of 10'x10' pop-up canopies for our son's wedding a couple of years ago and the night before, a strong wind knocked them over. One of them ended up ripping the cover in a couple of places, so we replaced it with a new one.
They didn't want to accept it and said "It was already old, and this one is new!"
"Yep, and we appreciated you allowing us to use it, and it's our responsibility to give you this new one. Now shut up, put it in your garage, and let's have a beer."