So, by your logic every man/woman actor that did not enlist and fight on the front lines was not a great American? Some that did saw combat and performed admirably others made films while in the military, are they not great?
A great many of them that did not enlist made films, entertained troops on leave, and sold war bonds. That did a lot for morale and war finance.
No by my logic, more is required to be termed “great”.
Was John Wayne patriotic? It seems so. But I would say being patriotic is good but not great.