It's false. People will not go into suspend mode when not walking; they still burn calories. A very large person would burn about 130 calories walking a mile. i.e. one large latte. And most people who are this large are not at risk of a caloric deficit by burning an extra 130 calories.
I agree that OP's assertion sounds dubious (especially considering the entire supply chain) but calories are a measure of energy, not CO2. You need to know the rate of CO2 emitted per kcal.
I'm not claiming that the CO2 exhaled by people is relevant. I'm claiming that growing food requires significant energy inputs unless you want to go back to the world where most human labor went into growing food.
The problem that this is the wrong measure to use emissions per mile, when it's really about emissions per trip.
A car flying down the freeway uses less emissions per mile, but if one is traveling 50 miles versus just walking to down the block the former is using a lot more emissions even if it is more efficient per mile.
Do you have a source for this? Sounds questionable.