On the 2 occasions I've had a screen replaced by a main dealer, they've called in Autoglass or National Windscreens anyway. They certainly didnt fit it themselves and nor would I want them to.
Would you prefer someone who fits windscreens all day every day or a grease monkey who fits 2 a year?
You are well within your rights to request your insurer to use OEM glass. There maybe some clauses to exclude this if the car is outside manufacturers warranty, but if its within it, you are entitled to OEM glass and any parts to be OEM.
The insurance ombudsman would be on your side.