I'm not clear as to what happened with Hamilton's fuel, did they not give him enough to finish the race in full speed mode or something?
I don't think this is the case, teams always make sure to put in the exact amount of fuel required to finish the race under normal conditions but not have any left afterwards, as that would be just ballast. I can only assume that Hamilton found himself around some more fuel-sapping situation than usual, thus causing him this fuel shortage problem during the later stages of the race.
And yes this means that Brawnhammer's excuse that both cars must end the race in 1 piece does not hold any water, when you are on fuel saving mode you are way slower than any car behind you, Brawn just wanted to keep tensions low within his team. This doesn't mean I believe that maintaining the status quo between teammates during the dying stages of the race is not a good strategy, because I think it is.