That doesn't make any sense to me - if I am already using all my muscle strength to push down to propel the bike forward with my right leg, where do I get the extra strength to lift the left leg. The weight of the left leg is then effectively pushing against my forward motion by requiring some of the work from my right leg to lift it up. On the other hand, if I lift my left leg with my hamstrings (that is why they are there after all) then all the work of my right leg can go into moving the bike forward.

One leg drills or riding with special cranks that allow each leg to operate independantly will show that you can and do pull up with the opposite leg. In general practive this is highly dependant on cadence. The quadraceps are stronger and react faster than the hamstrings, epecially in untrained riders. At high cadences, where most of those lab tests are done, the hamstrings are not able to balance the quads and so there isn't much "pull up" effect. At low cadences, like when climbing a hill, the hamstrings play a much larger role. I can pedal with no pushing at all, just pulling up although it isn't very efficient. In practice I have to rachet down my shoes and tighten the velco straps to keep from pulling out on climbs and when I ride my commuter that has platforms my feet do sometimes slip off the pedals on the upstroke so that pretty much convinces me.