More likely they are fleeing since they are largely unarmed peasants, who can’t stand up to trained, armed, and armored soldiers.

And when they flee they take some of their food supplies with them and hide the rest. Foraging army might be able to find some of it, but rarely all. Also, if you are in enemy territory it is entirely possible to completely miss some remote village. It's not like they have a satellite map.

>>And when they flee they take some of their food supplies with them and hide the rest

YUP!

And beyond that, what they can't take or hide, they may very well burn to slow down the advance

Just because you have advance spies and they report existing supplies, you just cannot count on having those available when the full infantry arrives.

Burning cropland behind retreating troops is the tactic used to deal with "just taking theirs".