Yes, that is quite the plot hole. Didn't actually think about that one.
Still love the film though.
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My memory of quite how it unfolds is a little hazy now, but it smacks a bit of last-minute script redraft fucking it all up. Particularly as, for the most part, he's looking for the archaeologically appropriate El Dorado, and not aliens. But you can't deny the fact that right at the very start it's revealed he was hired by the US Government to take a look at alien corpses and saucer wreckage and that makes no sense at all.