The Lightning and the Jaguar (I believe Graham flew the Jag in the RAF) are classic swept wing supersonic fast jets where, when the angle of attack goes past what would be the stall in a straight wing aircraft, drag increases massively but lift remains, and may even increase. If sufficient thrust is available in a clean aircraft (e.g. reheat), recovery may be possible. The Hawk, IIRC, does lose lift in the heavy buffet, and of course does not have reheat.
There is a tendency under severe stress for the human brain to do what it knows best, rather than what is correct. Thus pilots can "revert to type" and fly the way they did in the aircraft they know best, rather than the way they should in the one they are in.
I am not saying this is what happened, but it is something investigators consider.
LJ - Beers - I believe he did!