Lancelot has the key issue diagnosed. It is the gash nature of most GA pilots that caused this incident. Transition altitude and RT had absolutely nothing to do with it. They paid no attention to the clearance, the charts or terrain and just blasted off in a cavalier fashion. Airline pilots operating from airports with a lot of GA see this sort of crap daily - I saw a biz jet out of a London airport declare an emergency as he got airborne, bringing all departures in the London TMA to a halt for 30 minutes, because of an "FMS malfunction". He was only positioning to Farnborough, FFS! He clearly got airborne with the FMS misset or not set at all, with no raw data back ups and no mental preparation for the SID. London had to bring in the whole "hectopascal" read back because of GA pilots assuming everything is done in inches all over. I would regularly see the biz jets nearly run off the end, and one time actually do so, landing on wet runways with the thrust up to get a greaser.
That is the issue here. Not US/Europe, not transition levels, not RT. GA attitudes.