True, the likelihood that two randomly generated sequences would have nearly identical 64 bases is very small. But genomes aren't random. You would need to know more about what the region does to make the argument convincing.

A toy example would be if the sequence belongs to a mobile genetic element - it would be very plausible that it comes from two different loci. Same goes for genes from large gene families with deeply conserved regions or genes that have recently undergone duplication, etc.

Thanks Pieter - this is what I suspected. My PI and I are discussing the need to sequence a reference genome and what we would gain by pushing that forward. Cheers!