Vajda shows that the abstract forms of lexical and grammatical morphemes and the rules of composition of the Ket verb find systematic and numerous parallels in the Na-Dene protolanguage reconstructed to account for the modern Tlingit and Eyak languages and the Athabaskan language family (whose daughters include Gwich’in, Koyukon, Dena’ina and others of Alaska, Hupa of California, and Navajo of the U.S. Southwest). [...] The comparison also shows conclusively that Haida, sometimes associated with Na-Dene, is not related.
It lists a long list of linguists who’re supportive, so it looks like it’s quite safe.
We’re really talking about huge distances here, by the way. I’ve made a wee map using Google Maps to demonstrate: