I can't recall the exact language in the CFA packet, but I can tell you admissions isn't that picky. They aren't going to call the coach and verify the credentials.
Candidate Fitness Assessment (CFA):
You must pass the CFA, an evaluation of your physical fitness, before your name will be forwarded to DoDMERB to schedule your medical examination. The CFA may be administered by a Physical Education Teacher, J/ROTC instructor, Academy Field Representative, or any commissioned/non-commissioned officer other than a parent/guardian.