I have seen this in practice but not often enough to say that is the norm i.e. short labour means long third stage.
My own thoughts are that the administration of a drug to manage the third stage throws things into disarray. Since the body has been capable of delivering the baby in a short time, why should it be necessary to still routinely 'actively manage' the third stage which is what we hospital midwives tend to do in accordance with hospital policy. In the absence of bleeding, a physiological third stage can take as long as 2 hours safely. However, left to it's own devices, nature can have the placenta delivered physiologically within 10 minutes.
My question would be, does the administration of an oxytocic drug routinely for the third stage make the third stage longer in a quick labour by interefering with the physiological process?