If Bob, a private pilot, is not logging flight time, what are the limits on reimbursement? In this case, can he be reimbursed for 100% of the expense of the flight, but no more?
The hypothetical exchange is something like this:
Pilot holding a PPL: I want to be paid to fly somebody/something from A to B.
FAA: You can't. Paying money is obviously compensation and the PPL generally doesn't allow you to fly for compensation. (FAR 61.113)
Pilot: OK, what about if somebody paid all the operating expenses instead?
FAA: You're getting compensated because you got to go from A to B for free. You have to pay your fair share of the expenses. (FAR 61.113(c))
Pilot: OK, what if they're letting me use their plane for free? It's banner towing or glider towing, so I don't get a free trip anywhere.
FAA: Why would you want to fly their plane in circles for free?
Pilot: I can log hours.
FAA: That's compensation. Those hours have an obvious value to you for your future airline pilot job. Otherwise why would you provide labor?
Pilot: What can I do in that situation?
FAA: Don't log the hours. Then the flying is totally worthless to you, so you're not being compensated.
Pilot: Nuts to that. I'm not flying a banner around for no money or logbook hours.
FAA: Mission accomplished.
The key is in the linked scenario, the pilot is providing their labor for free because they are receiving logbook hours. The logbook hours have value, so that's compensation, just like cash. Not logging hours (in this scenario) is just like not accepting cash: you can't take either.
Nothing in the CFRs say you can be compensated at 100% as long as you don't log the time.
The standard is: "A private pilot may not pay less than the pro rata share of the operating expenses of a flight with passengers, provided the expenses involve only fuel, oil, airport expenditures, or rental fees."
There are a few exceptions, but they don’t have anything to do with not logging time.