Sure they could steal a cache... but they had to find it.
It's not like having an all access pass to foods through out the year.
Tubers stores go bad at a certain point in the year... they rot, or begin to grow again, thus cutting consumption off for a time.
For early man to forage more than he could consume for a few days at best and safely store it, without attracting other animals, is just unlikely.
Dairy is neolithic... not paleo. I'm sure that's why you deleted all of that though.
Also... Lewis' post --"stable isotope analysis on bone shows that these people were eating at the top of the food chain, actually similar to an Arctic fox."
The scientific analysis shows that early humans were eating mostly animal products.