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[Star Wars] Did Uncle Owen accidentally make Luke Skywalker more curious about old Ben Kenobi by saying Obi-Wan died at the same time as Anakin?

Why would Uncle Owen know when some random person in a big galaxy died if Owen's position was that R2D2 was speaking nonsense? Wouldn't it make Luke suspicious that Owen is hiding something?

Luke Skywalker: Well, I stumbled across a recording while I was cleaning him. He says that he belongs to someone called Obi-Wan Kenobi. I thought he might have meant old Ben. Do you know what he's talking about? I wonder if he's related to Ben.
Uncle Owen: That wizard's just a crazy old man. You stay away from him, you hear me? He's dangerous. Now, tomorrow I want you to take that R2 unit to Anchorhead and have its memory erased. That'll be the end of it. It belongs to us now.
Luke Skywalker: But what if this Obi-Wan comes here looking for him?
Uncle Owen: He won't. I don't think he exists anymore. He died about the same time as your father.
Luke Skywalker: Did he know my father?
Uncle Owen: I told you to forget it.
gpt
It was probably the hologram of a space princess begging for help that really inspired his call to adventure. Before that he was helping his family be moisture farmers and was hoping to join the Empire, all around a boring life without much introspection. Not the type to be curious about a detail like that (especially since a lot of people died at the same time during those wars).