DISCLAIMER: This really only applies to Nimitz-Class CVN life. SSN life doesn't really afford the facilities to stay in shape with an aggressive OPTEMPO.
For what it's worth (at least where I'm currently working -- world's finest east coast CVN), folks aren't getting kicked out for PRT failures. Sure, they are ineligible to transfer and their careers get torpedoed when evals are capped at "significant problems," but they can serve their enlistments and separate with honorable discharges at the end.
Fitness in the Navy comes down to time management on individual and divisional levels. If you present a plan to your chain of command and DEMONSTRATE RESULTS, you don't have to meet up with the department on a softball field to do calisthenics ankle deep in goose poo. If you have a chubby bunny in your work center, he/she doesn't even necessarily have to attend the largely ineffective FEP sessions. My division right now is big into fitness. We have a few people struggling with body fat. We worked together with the chain of command to allow the heftier fellers to avoid FEP, instead going to the weight room with the avid lifters. Instead of doing four-count calf raises people get a real workout. Instead of keeping a silly diet journal (apparently now part of FEP) people get to burn the calories they eat.
We manage to do this while maintaining a pretty demanding OPTEMPO and a five-and-dime watch rotation, because we're willing to work together as a team (augmenting watches whenever allowed and having an "accountabilibuddy" system) to make sure everybody gets time to work out. We're probably the only CVN division in existence that doesn't accept "that's not my job" as an answer to operational and maintenance tasking, because we work together to get our s**t done so we can go to the gym.
Strangely enough, by working out together we also wind up being a more cohesive group in general. We do pretty damn well on inspections and VIP visits because we don't lock ourselves into our collateral duty based specialties. I see other divisions standing around in their spaces, waiting on others to finish "their" work so they can all go home (or to berthing, etc.). We get together and git-r-done so we can go to the gym.
I guess I'm getting at the idea that, while I don't think being chubby makes a person a worse operator/technician, embracing the buzzword "culture of fitness" seems to make a group/unit/workcenter tighter. In addition to looking and feeling better, improved confidence and divisional morale; it could be argued that people who take better care of themselves sometimes take better care of their responsibilities. When 80% of the force is between the ages of 20 and 26 and required to be healthy enough for physical activity, there's not a real reason to be out of shape on an A4W ship (sea-going -- shipyard is a whole other animal, requiring a greater deliberate effort to stay in shape) and out of shape. It just takes an honest effort from the division to keep everyone healthy. If 100% of your division is not on the watchbill and you have PRT failures, one could suggest that the failure itself was a team effort.
/pep talk, rant, soapbox, high horse