I've never worked for the AAIB but I applied once! I also knew a couple of people who worked there.
Extensive experience means just that, I think you will find. I would guess that degree plus ten years hands-on is roughly what they are aiming at. I did 16 years in the RAF as an engineer officer and had experience of accident investigation - that seemed to be the sort of thing that put me in the frame, but without success.
I think you will find that the jobs they do advertise (on Capita RAS) are heavily oversubscribed and so they are less likely to take someone who has little experience (like any other job).