Besides, if we go back to the entirely debate of "Is Edi the normandy now?" then Edi controls the ship, and what sheppard and the alliance do is to enslave her. She should have free reign and do what she wants.
Yes, the EDI thing is one good example.
It's up to the player. The overt narrative does push one thing more than other things (ME1 - Spectre, ME2 - Cerberus, ME3 - Alliance), but there are plenty of reasonings to back up whatever your personal decision is.
One could, and some people very well do, consider the ship to not be Alliance anymore, but EDI personified, and all those soldiers on board to be passengers for her to take care of, but not to take the ship 'from' her (since it 'is' her).
Or one could consider it 'Shepard's' ship above all else, and that it just has affiliation with the Alliance currently.
Or one could consider it the Alliance's ship, still, above all else. This is the more in-your-face one, unless you go all super Paragon about it - in which case you'll hear a lot more lines focusing on the awesome Shepard leader than his dedication to the Alliance.