Aren't we talking about an environment where there are rampant cheaters? My perception was that this is by definition a low-trust company. Of course, it is always going to be easier to remove yourself from that situation and go to a company that has more rigorous interviews that would catch cheating in the first place.
The corollary of your argument is that hiring rampant cheaters produces (by definition, as you say) a low-trust company. Putting aside everything else, low-trust organizations are intrinsically dysfunctional (though it may take a while for the consequences to play out.) In them, asking more questions will not get you useful information, and you had better watch your back.
See, for example, the Third Reich, the Soviet Union, Hoxha's Albania, the Taliban's Afghanistan...
