(if less or equal then the price of the base airport)
That's unfair. If fuel is cheaper elsewhere, then
the owner makes a profit. If the fuel is more expensive elsewhere, then
you pay the loss.
Either the owner pays for the fuel outright, no matter the cost, or you pay for the fuel, no matter the cost, and you get reimbursed according to the rate at the aircrafts home base. The latter solution is the most common, and most fair.
It's good for the owner because they know exactly what their fuel is going to cost, and can base the "wet" rate on that. And it's good for you since it motivates you to find the bargains. Or, at the very least, avoid the really expensive places.
BTW 170 euro per hour wet doesn't sound too bad. At my club we pay significantly more. But as others have said, you've got an appointment to keep. Being *on time* for that appointment is far more important than getting there under your own steam. Money aside, cases like this I simply fly commercially, and save the money for flying somewhere myself when I'm not under any time pressure.