As if the government would ever pay for full solutions to the problem; in regards to treatment.
Ah, you mean killing the sickly? (joke)
I think in order for anyone in a position to consider adding gym membership as a cost reducing means towards reducing medical costs, there would have to be multiple substantial (expensive) studies done. There are a lot of factors to consider, including injuries that occur at the gym, how much going to the gym X amount of times for Y amount of time doing Z type of exercise would decrease the risk of T number of common and expensive to treat diseases. You'd need to select groups of thousands of people from all each age group in the US for each variable change, and you'd need a sizable control group. You'd also need to observe them for... maybe 50 years?
I think this sort of thing is ripe for abuse though. As 'just going' to the gym doesn't really mean anything. I could just swipe into the gym and then just leave, within all of 15-20 minutes.
I see where you're coming from here, though I do think it'd be better to support education for people into healthy eating and the importance of working out rather then subsidizing businesses into making more and more money. Education has a much better payoff for us rather then shareholders just wanting their company to lobby for government subsidizes.
I don't know what incentive you'd get out of abusing the system? If someone is handing out free gym memberships to all of their members and you grab one just to skew their data I suppose? There wouldn't be any direct financial benefit. I suppose you'd make your insurance company pay an extra $10 per month, maybe less as I'm sure the insurance companies could A. open their own gym facilities or B. negotiate some crazy low rates for signing up a million members.