I think your classmate needs to recheck the definition of a Mary Sue first.
A Mary Sue is a type of fictional character, usually a young woman, who is portrayed as unrealistically free of weaknesses. Originating in fan fiction, a Mary Sue is often an author's idealized self-insertion.
To me, it sounds like they are jealous 
I don't mind self-inserts, they are bound to happen, but I think we all, or at least the majority of us, dislike Mary Sue characters.
Also for the naming thing, where I am from, it's actually common for cousins to have the same name if the families have a lot of kids and they maintain close relationships. At large family gatherings I attend, I am sure there are at least 4 Christophers on the dinner table. It was my grandfather's name. I see it less and less with the children my cousins are having (as in the next generation) but the generation before us did it often from my personal experience 