This is a very good point! Alternately, perhaps they weren't the ones who *built* the spaceship. Perhaps they never knew more than the basics of how to maintain it for long enough to reach their destination (if they even had one and weren't just flying away from something, rather than to something).
Ooh, so a third species gave them the spaceship so they could escape? (Or, more sinisterly, so they could invade Earth. Or so they could be used as slaves by a member of that third race.) Now I want to see the angry spaceship rental agent come and try to get it back... *g*

Remembering flashes of a life the character never lived, along with the resulting identity issues, could be a very nice element in a story, I think.
It would, but I think I like them best in a context other than reincarnation – have them be clearly scenes from someone else's life with magical memory implantation or Hallows handwaving or something, instead of this ... "oh but you're a reincarnation, so you're technically sort of the same person". Commit or get out, none of this half-way stuff!