It has as much significance as a Christmas Card, really.
I get one from my insurance agent every year, among others. The question is one of if she was the only one in the class to get one. If that can be proven, maybe there is something to it. Her parents knew him, she likely sent him an announcement, and he sent her a card with a note. It doesn't mean he handed it to her.
Bingo! I was a teen in the 70's. I suppose I might be able to find my graduation cards. I would not expect whomever sent them to remember meeting me at a church function or band concert or that my folks had me send an announcement. I have to admit, I do not remember everyone I dated 40 years ago. I also know I had a crush on someone much older(OK, only 10 years older) and was thrilled to get a card. I doubt he would remember me. lol
I went back to where I grew up this summer. People assumed I knew them (very small town) and I had no clue. I nodded a lot but if you said to me "hey, Tom Smith really was happy to see you at the park this summer", I would probably look at you with a blank stare.
Roy Moore likely knew a lot of people and sent a lot of cards. Maybe even went out with some of them but not recall them. I do not see this as a lie or whatever; it is pretty normal in my opinion.