Re: "I assume there was some backstage arm-twisting"
Personally, I think there was probably a lot of shouting of "Don't be so fucking stupid! Now get back out there and tell people how wrong you were!"
Much as I'd like to agree with you, the technical people on a show like that are rarely in a position to be allowed near the "talent", never mind speak the truth to them. All the "important" people are media and arts graduates. I'd bet the order to apologise came from outside the immediate production crew or bosses.
Biting the hand that feeds IT
