Going back to the first page, Brian and Campag were both correct.

The glutes are the most powerful muscle in the legs, and as such offer the most potential force. But, many people do not actively engage their glutes, and it takes effort for most people to learn how to maximize their glute usage in a pedal stroke. Hence, they end up relying predominantly on their quads, which are not as powerful.

The key is to learn how to maximize the use of glutes, hamstrings, hip flexors AND quads. Glutes push the pedal down, hamstrings pull the pedal back, hip flexors pull the pedal up, quads push the pedal over the top. This is why one-legged drills are so important.