I know they have their own vans because a chap attended in one when my wife ripped a tyre off my car on a freezing winter night. I was an hour away driving home, put a call into them and at first they said they be there within 30 minutes. Lone female, in a black car, on an unlit national speed limit country road, just after a bend. A horrid situation, which after 25 minutes (I'm driving at a pace to get to collect our son by this point, which is where she'd been going), they ring to ask if my wife has ID on her. I call my wife who said no, she'd not taken her handbag as she was just going to collect out boy. I relayed that to Green Flag who then said that despite it being my car, which was specifically registered on the policy (i.e. it covered my vehicles, not us personally), if my wife couldn't produce ID they would charge us £110 call out and as it stood they'd called off the recovery driver! Short version, I went loopy, they reinstated the call out and the chap got to my wife and about 30 seconds before I did. He turned up in a fully liveried Green Flag Transit van and was a decent bloke, but said he had no record of the first call out and thinks control we're just stalling for time. Whatever the reason, it left a very bitter taste in our mouths.
The other time I called them out was an electrical problem and they sent some random scruffy low loader with a driver who looked (and smelt) like something from a Madmax film.