While I think that “mayday” for a low fuel state (as opposed to knowing that you will run out of the stuff) is mis-use of the term as it was originally intended, that is what the regulations required in this case.
Correct.
All this was discussed, at length, when the new regulations were made. The use of the word 'mayday' is now mandated in circumstances that are not an emergency. In reality the circumstances might justify a 'pan' call, but the brains trust that makes the rules knows better.
Don't forget: If you're doing circuits and you realise you might land with less than 30 minutes' fuel remaining, you must declare a 'mayday'.