I wouldn't be worried about not taking money because if you do get into med school it's pretty likely they will accept you. The higher probability of disappointment occurs when you do take the money and do not get into med school. At that point you would be "needs of the Navy" status.
The point is, until you have a solid GPA and MCAT I wouldn't even worry about that far ahead. If you do plan on doing NROTC or something just realize the chances of getting into med school are rather low and you have no problem serving the Navy in another capacity then you will be fine.
What's your current status right now? HS? College? NROTC?
Also remember that the Army has a much larger medical department and thus a lot more slots, residencies and training opportunities.
EDIT: A couple weeks ago you asked a question about being a pilot in the various services. Just curious do you want to be a physician or pilot? Med school is hardly a secondary path with all the competition around the nation that is and isn't in ROTC.