I quite agree about the headcount. But then crew can get it wrong, I know this from watching a departing flight lining up when a gezzer turns up a the desk saying "I was asleep, is that my plane?"
It all depends on how the airline manage the turnround. FR crew I am told follow the pax up the aircraft doing the security check so as the last one gets off they are ready for boarding. The flight crew do the loadsheet and have plenty of gate staff.
I dont know how Jet2 manage thier turnrounds but I have my overall impression of the industry in general, not just one specific airline!!!