What reason is there to doubt the claims being made in the paper?

There are plenty of reasons. First off, as Mark Carnall from the Oxford University Museum of Natural History pointed out in a series of tweets, not one of the paper’s authors is a zoologist.

Much of the authors’ speculation rests on the idea that the genetics of octopuses and their relatives are mysterious – yet a 2015 paper published in Nature revealed the octopus genome, so this is rather disingenuous.

In fact, octopus genes suggest they fit into the generally understood theory of the evolution of life on Earth, and require no alien invasion. They are thought to have split from the squid lineage around 135 million years ago.

Molecular geneticist Professor Karin Moelling of the Max Planck Institute Molecular Genetics, who was asked to review the report, concluded that it "cannot be taken seriously”.