His theory is that in the ancestral environment, we needed to do a lot of sprinting to catch things or avoid being caught, with relatively less long/slow exercise. (Also, that training for recovery after short bursts of exercises increases lung capacity and heart health more quickly.)

This strikes me as very unlikely, given that humans have lower sprinting speeds than most prey and predator animals, but better endurance capabilities, enabling us to catch them through persistence hunting. Humans have adaptations that make us quite good at steady long distance running, such as an energy-conserving bipedal gait and highly efficient cooling through sweat, but compared to other animals our size we're quite bad at covering short distances quickly. The idea that our ancestral environment demanded a lot of sprinting relative to long distance running sounds downright implausible.