I believe that you'll find that most reputable and responsible firearms training institutions which are accesible to non military and LE, including Insights and FAS, have very similar personal reference requirements. This requirement seems even to be specified in the web site reference that you gave.
Though I'm not completely familiar with WA state 'shall issue' statutes I'm fairly certain that a WA CCW permit is one of the easiest to obtain. Therefore, character affirmation through this method is hardly an insurmountable obstacle to admission to formal firearms training.
Also, I could be mistaken but I don't think that Marty Hayes' LE background includes service with a Southern California agency if that was what you meant by "SoCal LEO".