wrong:
"Although a person's enlistment in the armed forces of a foreign country may not constitute a violation of U.S. law, it could subject him or her to Section 349(a)(3) of the Immigration and Nationality Act [8 U.S.C. 1481(a)(3)] which provides for loss of U.S. nationality if an American voluntarily and with the intention of relinquishing U.S. citizenship enters or serves in foreign armed forces engaged in hostilities against the United States or serves in the armed forces of any foreign country as a commissioned or non-commissioned officer."
from the state dept
LOSS OF CITIZENSHIP: Under certain circumstances, you may lose your U.S. citizenship by performing any of the following acts: (1) being naturalized in a foreign state; (2) taking an oath or making a declaration to a foreign state; (3) serving in the armed forces of a foreign state; [does not require that it be against the U.S.] (4) accepting employment with a foreign government; or (5) formally renouncing U.S. citizenship before a U.S. consular officer overseas. For detailed infformation, consult the nearest American Embassy or Consulate, or contact the Office of Citizens Consular Services, Department of State, Washington, DC 20520-4818, or call (202) 647-3444.
There is the "may lose" requirement, which I guess would encompass the "intent" requirement you've cited. However, my guess is that Walker had much easier access to his passport than he did do to the state department website. Therefore, I would argue that he was aware that his actions would result in a possible, and perhaps definite, loss of citizenship.
At any rate, it would not require a formal renunciation, as was declared in the original post to which I replied.