Reunited from maternity ward

(I've changed the specific names, but the story is, I believe, accurate). My mother was born in Scotland, in the next bed to a Jane Smith. Their mothers became friends, and the children played together growing up, since they happened to live nearby, until the Smiths moved to England when the girls were about four. My mother did a BA in Scotland, but a PhD at Elided College, Cambridge. Years later at an Elided reunion, she met someone who turned out to be Jane Smith, who had done her BA there - obviously, they'd not quite overlapped while actually attending. That would be a slight coincidence, but it turns out that my father, who also went to Cambridge, had one ex-girlfriend before meeting my mother... Jane Smith.