I think any young man at the time would have done whatever he could to get out of going to Vietnam.
Obviously it was easier for the wealthy and connected.
Not all folks that were drafted or enlisted were deployed to Viet Nam. Even some that requested duty there were denied. Others volunteered to do multiple tours there.
And many did. If that upsets Zumwalt or causes him to question a president's qualification to be commander-in-chief then so be it. But that belief will eliminate most of the politicians on both parties from being president.