Yes, the landing is relevant because his "SE Currency" was about to expire. The landing helps to delay that. Plus, a retractable gear aircraft isn't required for single engine currency. If that's all he wanted and the argument was made that he didn't get three landings, the FBO could argue that he should have just rented a warrior, 152 or whatever their fixed single trainer is. The landing helps...win.
He handled an abnormal and possible emergency situation without bending metal or hurting anyone. That's good for the experience bucket. There's no way you can have a loss there. That's win in itself.
He's now got a story to tell. That's good for when he gets his CFI and has students to teach or an interview when he gets the "tell me about a time when..." questions. It goes with experience. It's another win.
He's got some more flight time, which counts towards the ATP, which is a big deal. Particularly if he wants to do any professional flying. Again. Win.
So yes...I think the FBO would be justified in charging for the time per the rental agreement (depending on what that says). It's a win/win/win for the OP, why should the FBO be off the hook? If you're going to argue that they shouldn't be renting broken planes, then the rental rates just went through the roof to pay for mx every time a plane comes down. Just taxi right up to the mx hangar, they're going to do an annual on it every 1.2 so they can swing the gear, do some inspections and make sure they know they're renting a not-broken plane. No one wants that.
Plus, you have to realize...sometimes stuff just breaks. No one can explain it. It just happens. You deal and move on.
-mini