You are committed when you don't have enough fuel to fly anywhere else. That other place could be just around the corner or hours away. But not having enough fuel doesn't mean you you do not have options. Any fuel in the tanks can burnt, the argument should be about who does what paperwork. Once you are relieved of the decision of where to go you can now concentrate on how you are going to soend your fuel. For example, do you want to spend it holding? Or would you prefer to spend it preparing for an off airfield/tarmac arrival? There again you could spend it doing approaches. The choice is up to you. But after the trip is over, you would be wise spending a little time trying to work out whether you could have foreseen ending up in the position you found yourself.
PM