Not quit accurate...
Even so, there are gaps between fruits and tubers where the majority of forage-able foods would be green vegetation or mushrooms. or other less sugary/starchy type foods. And where foragers would rely on insect protein rather heavily rather than hunted meats.
And people groups were moving around quite a bit throughout out our evolution from quite early on as well... Not all of them lived in areas where specific tuber consumption is highest. Stop concentrating so much on single populations. Even near the equator there is a wide variance in foods and food availability. You act like there were just potatoes in the pantry every day. Not nearly the case.
Also there was not technology in relocation for early man... it was called group growth. An area or group can only support a certain number of people before either foods get scarce (also due to yearly shifts in climate) or due to group sized someone decided to move off and form his own group (splitting). People then walk. Yep... just walk a few miles in a new direction until a new good spot was found.
No one moved from the equator to cold climates in one fell swoop... it was gradual and over many generations adapting to small shifts as they moved incrementally.