I can only speak for Ryanair here in the UK/Europe but we are trained to recover from high altitude stalls and jet upsets amongst other things. I assume it's the same in every other major airline - can't see why it wouldn't be.
If the AF documentary you're watching is the same one we had over here a couple of days ago then I think the point they were trying to make was that military pilots spend there lives in unusual attitudes and are therefore more accustumed to the 'feel' of being in those situations and therefore theoretically would react quicker.