Clayton Cramer has this to say about the claim:
I find this claim implausible. Like nearly all human behavior changes caused by financial incentives, it operates at the margins. Where I live, the only regular destination that I can reach by foot rather than by car is my mailbox, which is a bit more than half a mile away. When I lived in West Boise, my job was 1 1/2 miles away. While I very occasionally walked or bicycled, cost was not a factor in the decision–simply because driving 1 1/2 miles was very, very cheap (about 3 1/2 gallons a month), and unless gasoline rose by $10 per gallon, the reduced driving cost was more than made up for with the inconvenience of not being to zip home to have lunch with my wife, and the cost of eating in the company cafeteria.
I agree. One of the great ironies for me, when I was actively biking last year, was that I was spending more gas to bike than I would have if I just stayed home.  I enjoy both cycling and hiking, and both of them, for me, involve taking my bike, or my feet and backpack somewhere that I can do it. I can cycle around my neighborhood, but that gets old. To leave the neighborhood on the roads around here is taking your life into your hands.
So for me, higher gas prices mean less hiking and cycling, and thus I get fatter, not thinner.
If the prices were high enough, it could take money out of your food budget and you’d lose that way.
Of course, I think most people would carpool rather than cut their food budget.
It makes sense in a your typical mega-urban locality like New York, Chicago, LA.
In most moderately sized cities, suburbs and rural areas, if it has any effect at all, your observations are probably accurate. People will simply participate in less recreational activities which will result in an overall decrease in exercise.
I know around here, there is a 7-11, a couple of gas stations and a couple of bars and a church within walking distance. Granted, the basic necessities of life are covered, but anything else requires transportation.
Considering that our public transportation “system” is about as efficient as digging a moat with a spoon, higher gas prices just means people stay home in front of the tube (or the computer in my case) more.