This subject of this post has an update! You can find the update here.
The cemetery of historical linguistics is littered with the graves of famous linguists who buried their careers by making unsupported (or even ridiculous) claims of genetic relationships between languages. Why, just the language behind Linear A is a veritable killing field. So when someone says that they can demonstrate that Basque is related to another language, needless to say my eyebrows rise a little.
It's understandable. People have claimed Basque related to North Caucasian, Etruscan, Minoan, Iberian, Proto-Indo-European, Proto-Afrasian, the list goes on. It's come to my attention that two days ago, Juliette Blevins, who is no academic slouch, made the astonishing claim at the University of Oslo's historical linguistics conference that it is possible to demonstrate that Basque and Proto-Indo-European are distantly related. Very distantly. But close enough that she was able to spot up to two hundred related items with systematic sound correspondences - including a relationship with the Indo-European laryngeals. For non-linguists out there, Proto-Indo-European is believed to have had three different "H" sounds, not one, that were lost in all Indo-European languages except in Hittite, Luwian, Palaic, and Lydian (extinct languages in what is modern-day Turkey).
Her abstract was very vague and looked like any other summary of Joseba Lakarra's work. Since the untimely death of the famous Vasconist R. L. Trask, Lakarra is probably the leading light of historical Basque language studies; summaries of Lakarra's work abound. If I were at the conference I probably would have skipped Blevins' talk, but people who attended inform me that this was no mere summary. Making the claim that it is possible to show that Basque and Proto-Indo-European are related is dangerous ground to tread. Forni recently made the claim in the Journal of Indo-European Studies earlier this year and his work was not well received - including a resounding rejection from Lakarra himself.
I will not pass judgment on Blevins' argument until I read it myself, but am I skeptical? Yes, definitely.