Well, I think there is something up with Naomi, I'm like sayid, and not trusting her at this point. Oddly though, I don't think Cooper is lying about this one, maybe she just misspoke, and got her island paradises mixed up.
However, if you were really trying to cover up the crash, you probably would put the fake wreckage FAR from the actual crash site, to throw off future investigations.
But I still don't trust her yet.