Obedience is better than sacrifice.
My

:
1. Was there any indication that the area was "content-neutral"? (Not that I think that's appropriate, but if there's no sign, then there's no reason to think the singing would be objectionable).
2. There are locations in our country (The Alamo, for one), where there ARE signs posted that instruct visitors that since this is a place where war heroes died, proper decorum means a quiet, reverent atmosphere. (Obviously the Lincoln Memorial is not such a site.)
3. It seems to me that if the students had re-located to the "proper" location and started again (even if it DID "spoil the moment"), they would have provided a very STRONG testimony by their obedience by also by their perseverance.
In conclusion, even though I think the rule of having a "content-neutral" site at a national monument is somewhat of an oxymoron, and don't agree with it, what do we demonstrate by our disobedience in this type of case? Even though the students were not fined, they could have been, which would not have served their futures well.
"Pick your battles" comes to mind. Singing in front of the Lincoln Memorial? Or refusing to go to the back of the bus?