He means that big national carriers like BA or LH are so big that they can say that we only take pilots from these schools etc. But he doesn´t think that companies like JET2 and Cityjet are so important that they can do so. What he means is who are they to say this?
Well Cityjet are owned by Air France, an airline that has over 100 more aircraft than BA so I would take his opinion with a pinch of salt.