I'm relying on my poor (so declares my wife) memory here, but I seem to recollect that this was a classic case of company pressure versus Captain's authority. The company encouraged the Captain to bring the a/c to MUC to minimize AOG time for the required maintenance. When the critical fuel situation became evident the a/c had just passed BUD and the crew calculated that the time to make the descent into BUD they could equally make it to VIE.
How often are we, in our respective jobs, confronted with the choice between safety and future career prospects within the company? If you stick to your guns in the name of safety you're labelled a trouble maker. If you appease your chiefs and screw up you're on your own!