Screening pilots is not that hard, however airlines HR and/or management current procedures may overlook something that the military do for some time prior to put a multi-million very lethal F-16/F-18/Mirage/Eurofighter/etc in the hands of someone.
There are not many stories of screwed up military pilots that crashed their warbird in the worst possible way. And at first glance most of those topgun military pilots seem a bit beyond of what you might consider ‘normal’.