No matter what the conclusion of the doctors at that institution was. No matter the reason for being committed.
Sorry, you're mistaken:
(3) APPLICATION TO PERSONS WHO HAVE BEEN ADJUDICATED AS A MENTAL DEFECTIVE OR COMMITTED TO A MENTAL INSTITUTION-(A) For purposes of paragraph (1), an adjudication as a mental defective occurs when a court, board, commission, or other government entity determines that a person, as a result of marked subnormal intelligence, or mental illness, incompetency, condition, or disease--
(i) is a danger to himself or to others; or
(ii) lacks the mental capacity to contract or manage his own affairs.
(B) The term `adjudicated as a mental defective' includes--
(i) a finding of insanity by a court in a criminal case; and
(ii) a finding that a person is incompetent to stand trial or is not guilty by reason of lack of mental responsibility pursuant to articles 50a and 72b of the Uniform Code of Military Justice (10 U.S.C. 850a, 876b).
(C) EXCEPTIONS- This paragraph does not apply to--
(i) a person--
(I) in a mental institution for observation; or
(II) voluntarily committed to a mental institution; or
(ii) information protected by doctor-patient privilege.