Wanting to save fuel is not a valid reason for not running the APU in this scenario, and I'd be very surprised if that's the reason. It doesn't take a rocket surgeon to realise the cost of negative publicity far outweighs the cost of even a very expensive uplift (I'm sure it wouldn't be too hard to get a tanker in from PMR). There must be some other reason such as an inoperative APU, although that seems unlikely on a MEL/WLG.
Maybe if the spin doctors gave a bit more factual information, the rumour mill wouldn't have to fill in the gaps!