This does not imply that, for example, a daily or weekly peak of energy expenditure was the same. As training once per week for 15 minutes with weights is enough to grow muscles, it could be that hunter/gatheres needed to release energy at the max level like running away from a lion much more often than we do nowdays and during those releases the brain also had to work hardest.
>during those releases the brain also had to work hardest
That is speculation, and is unintuitive. Why would the brain "work hardest" when running? Why would modern humans not exert the same forces during sport? Why would humans, the top group-oriented predator, run from a lion?
The data linked above shows that observed Physical Activity Levels and caloric use are comparable to modern day. Stop inserting your own assumptions into the data.
The data do not indicate that we experience the same need to work at max energy for brief periods of time as hunter/gatheres. Besides running away from predators in most efficient way, consider throwing оf javelins or stones during hunting. It requires a very precise muscle work at max energy after intense brain activity of target selection. Modern day life does not involve that, yet evolutionary this combination of brain/muscle work at peak could be advantageous.