Apparently some non citizens did serve in Vietnam. How some of them got drafted is unknown. In some cases the citizens in question arrived as young immigrants who were never naturalized by their parents.
One of the few areas that the right seems to agree on is reducing waiting periods for citizenship for people who served in the US military during a time of war.
These noncitizens who served are my heroes. They likely could have stated hey I am not a citizen. Then again as many came as small children where would they go. Had some of these people spoken up the military likely or should have done the right thing.
Maybe someday a historian will do a book on these unlikely heroes.