I don't think you understand the problem. I suspect that I have operated through Budapest more times than you have had hot dinners. On not one single occasion was I, or any of my crew, required to go through immigration and back out again during a tech stop.
If I were asked to make a guess at what is really going on at Budapest, I would be looking at local airfield politics.
Just imagine that a bunch of senior Malev captains had a beer on the odd occasion with the chaps in immigration in their local pub.
Suddenly, Malev goes bust and the unfortunate chaps who are now out of a job, quite understandibly, resent Ryanair moving in to what was their golden bowler until last week when the sh*t hit the fan.
The immigration guys can't get away with b*ggering up Lufthansa etc etc but they can get away with b*ggering up any Ryanair crew member who has had the audacity to be based in BUD.
This is local politics; no more, no less.