May be related, not “are very closely related.” There are some cognates between the two families. But no two languages that were separated for 10,000 years are very closely related.
Why do people get so attached to pet linguistic theories of all things that they feel the need to make up informants, forage sources, and generally lie in order to “prove” a claim that has literally no value if it’s not true? It’s totally plausible that the languages are related, and that’s awesome! But the evidence for them being mutually intelligible just isn’t there.
Well, it's remarkable if these languages are related, but even so, we're talking about two languages that diverged thousands of years ago, maybe 10k years. Probably in the same ballpark as Proto-Indo-European or even older.
That is, these two languages would be about as mutually intelligible as, say, English and Albanian, or less.
I have doubts as well. "Almost" may be carrying a heavy load there. People are just really good at communicating, face to face, over difficult barriers, particularly when they share cultural underpinnings. But I don't speak any language in the family, and can only go on what they say.
