Not for those reasons
Ah, and if humanity decides that saving the lives of their own innocent children is more important than not killing an innocent bird hatchling, then they don't deserve to take the training wheels off their bicycle! To me, that's the flaw in the episode, as this particular moral conundrum is unlikely for anyone to take seriously.
That the Moon's mass would change because of whether a creature is alive or dead - well, the Incredible Hulk has more mass than Bruce Banner, so this is a typical comic-book level scientific solecism. For the Doctor to leave the moral decision up to an individual representative of humanity - well, if he let the U.N. or the politicians decide it, the result would have been predictable, and where's the dramatic tension in that?
So it sounds to me like it's rubbish, all right, but not for the reasons, and not as bad rubbish, as the reviewer makes out.