The vaccination card is not a legally controlled document. You can legally copy one, but be aware of laws against forgery and perjury. Unless one got a shot at a VA clinic there would probably not be any records for verification.
Just an aside but regarding your Vietnam service, there are a huge amount of pictures of the 6/32 FA in Vietnam on FB under Big Guns of the Vietnam War. FYI
This is absolutely false in California, and most likely false in other States. The vaccination details are entered into various databases. I know this to be a fact because I was able to query my own digital record.
Incorrect. The lot numbers for the vaccines are on the card, and ultimately will be in the CDC and State databases, which will be cross referenced for verification.