I'm not convinced that's true, otherwise it would be very difficult to ride without foot retension, which millions of people do everyday. Without foot retension, the muscles groups of the recovery phase (shown in blue yellow and green) cannot move the pedals. They can only lift the foot off the pedal, or make the foot move with the pedal, but can't really contribute to pedaling, nonetheless it is possible to pedal smoothly without retention.
The figure posted above is greatly oversimplifed. Many of those muscle groups clearly work beyond the ranges shown. For instance, knee extensors can move the pedals through the 12 o'clock position, even without foot retention and ankle plantarflexors can move the pedals at least a few degrees past the 6 o'clock position.
There is probably a paper out there testing the role of various muscles used in the pedalling cycle, but I've never seen it.