I don't know any federal examiners whose APA dues are paid for by their agency.  None of the agencies I have ever worked for ever paid membership dues.  I am no longer a member, since I got nothing of value for my $125.00 dues.  It's a good ol' boys club with the same officers elected every time, who give each other the same awards year after year at their annual seminar.  Any perceived affiliation with the federal gov't is simply because some federal examiners are members.   There is no "controlling interest" over the APA.