You only got the last sentence right...
April 2003 - As most people didn't know until a month ago, the military welcomes enlistment of non-citizens; more than 37,000 lawful permanent residents (green-card holders) serve in the military, where they account for about three percent of active-duty personnel.
There are certain restrictions. You have to be a citizen to become an officer or join certain units, like the Navy SEALs. And, depending on the branch of the service, non-citizens may only be able to serve for one term (Air Force) or for a maximum of eight years (Army).
Such limitations implicitly acknowledge the fact that a member of a republic's armed forces ought to be a citizen of that republic. The naturalization law reinforces this notion by abbreviating the residency requirement from five years to three for non-citizens on active duty. And the president last year exercised his statutory authority by issuing an executive order waiving the residency requirement altogether for people on active duty in time of war.