the point of stretching prior to a workout is to correct postural/movement deviations for a particular exercise or exercises. the problem with this is that relaxation stretching or static stretches held for a period of time can tend to slow the nervous system down or tell it to relax. then going into an exercise you now have to rev the CNS back up again. its a power struggle between slow down and speed up.
during a workout, the same is in effect. the point of stretching in a workout would be more of a dynamic ROM type stretch. short quick stretches, which keep the CNS primed up. long held relaxation stretches would again slow down the CNS. the only point of stretching during an exercise would be to stretch the OPPOSITE bodypart in order to reduce inhibition from tension. ie, stretch the lats to better do shoulder presses.
if their overall argument is to increase flexibility, mention the fact that functional or adequate flexibilty is all that is necessary to complete the motion without hyperlaxity in the joint (some tension is necessary to maintain joint stability). hyperflexibility can be detrimental to an individual based on what their goal is, and the newfound need to create strength in this new range of motion.
there is some good information out there regarding stretching, the need to do it, when to do it etc.