Not that it will help you, but a quick explanation;
Most of the time ( not always though!) it is NOT penny pinching by the FBO or flight school.
Depending on the deal they have with their fuel supplier they can get a discount when buying fuel in bulk.
So if the FBO/school pays $3/gallon they will (and should) reimburse $3/gallon.
You rent the aircraft wet, which means fuel included. At the price the FBO has paid which is fair.
If you decide to refuel somewhere and pay $5/gallon they cannot reimburse you for that amount. It will come out of their own revenue. Bad business idea.
It therefore really adds up if you don't plan your flights correctly.
Large airports charge more for the lease on underground tanks and FBO facilities, hence the fuel price has to go up.
With carefull planning you can end up not paying anything additional for the fuel.