The really relevant line is buried in a long sequence of Gwen's so even if he did rewatch something it probably wouldn't be that.
Jack Harkness isn't actually the name he was born with, which isn't too surprising if you think about it for long. He got that name from an American WWII soldier who was killed in action on a mission after being stationed in the UK. Except when Gwen was trying to research Torchwood she looked up his name and the files said he'd gone missing, specifically that he just didn't check in one morning, completely vanished, never been seen since. I'm pretty sure the discrepancy is because a while after Gwen joined, Jack and Tosh slipped back through time to 1941 to when that Jack was here. Jack met him and they had... a very obvious, very public moment, in front of his whole unit. So it looks like he's gone and changed the timeline and the original Jack instead disappeared sometime between Jack and Tosh returning to the present that night and the next morning, before the mission he was supposed to die on.
I mean, technically, he died either way. But somehow I don't think Jack would see it that way.