Anything is possible, but it's also easy to get lost in your eagerness — as I've also done many times myself XD
Things like Basque are so "attractive" to this kind of overzealous imagination and speculation for the very simple fact that we don't know. I'm not trying to be a partypooper or reject any counterideas without consideration — just that from experience, from my own and others' mistakes, I can see how in this case modesty and carefulness is a virtue.
(EDIT)
Though, I have to admit, I might be a tad sensitised when it comes to this particular topic. I've had the great unfortune of having some migraine-inducing arguments with some truly outrageous Finnic ultranationalist anthropologists, so the idea of Sami and Finns being special is nothing new — in particular being Europe's oldest people who ruled all of Europe before the "Russians" (PIE people) invaded from the east and oppressed the great Finnic people. Germanics, Celtics, Italics, Hellenics, Baltics, Slavics, these are the descendants of ancient Finnic mothers being raped by the invading oppressors, and Sami and Finns are the only true people of Europe, bla bla bla bla bla ...
*sigh*
Linguistics and anthropology has its fair share of crackpots as well :/