Good point, but how do you do a complete background check on someone who has only been in the U.S. for two years and spent the first 20 in Lahore, Pakistan (like one guy I recently served with)? Answer: You can't.
An incomplete background check is the same as a failed background check.
Those who fail background checks should be denied positions of trust and responsibility. If they are from any group, not just a profiled group, I would deny them any entrance to the military or to other positions of trust & responsibility BECAUSE they will have been ASKED to assist in completing a total background check. If they will not assist to the total satisfaction of all questions, then they have self-disqualified.