As I said, it was sloppy writing on my part. I wrote "The Celts" when I meant "The people of the British Isles". What you need to remember is that the movement of a language and culture does not necessarily require a replacement of the existing population. Indeed, Robert Drews argues that the spread of the I-E languages was performed largely by small groups of people who spread their culture to, and mixed with, indiginous populations, much as this article argues that the spread of Anglo-Saxon culture into the British Isles was more a matter of language and culture than genetics.
There were a lot of non-IE European languages including Basque, Finnish, Hungarian, Etruscan, and possibly Pictish. Most were replaced by various Indo-European dialects, much as I-E languages took over Anatolia, Persia, and Nothern India. Since Celtic language and culture migrated into British Isles and since the Scots are genetically linked to the Basques, it makes some sense to assume that pre-Celtic Scots spoke a language in the same family as Basque or that the Celts that migrated into Scotland spoke some sort of Basque-related language before becoming Celts.
