Michael isn't merely making the choice not to give Terri food and water himself, though; rather, he's seeking to prevent anyone else from providing it.
If you pick up a cat from a shelter, you are accepting the responsibility of providing a certain level of care for that cat. Severe neglect is punishable by law. That does not mean, though, that you're obligated for life to provide for the animal. If you become unable to care for it yourself you are allowed to either find someone else to care for it or return it to the shelter and let the shelter try to find someone (which they may or may not manage to do).
In short, you're not required to care for the animal yourself, but that does not give you the right to prevent others from doing so.
Should Michael's "property interest" in Terri exceed that of a cat owner over his pet?
Perhaps he really believes that Terri wanted to die if she should have gotten into this state. I think I might want to also, were I in her place.