Actually, that is - somewhat - a common misconception, to think of the Basques associated with the modern Basque country. The language boundary in Antiquity was a very different one, but it seems that Aquitanian (or 'Old Basque', if you will) was spoken in (in modern areas) Navarre, northern Aragon (on the Spanish side) as well as in Aquitania (south of the Garonne river). This is very clear from Aquitanian personal names and place names.
It is true that the area of the modern Basque Country (Euskadi / Pais Vasco) was Celtic in the time of the Romans, but that does not mean that the Basques were recent immigrants in Western Europe.
That I agree on (I also find it doubtful that Basque was originally a language of hunter-gatherers), which takes me to the next point (see below)...
This is wrong. Yes, in the Antiquity, the Basques were bordered to the north (Gauls) and Celtiberians (west), both obviously Celtic (and obviously Indo-European, by extension). But in the east, Old Basque speakers very clearly bordered onto speakers of Iberian, and likewise very clearly, there was a common lexicon of Iberian and Aquitanian (an often cited example is Iberian 'ili-' and Basque 'hiri', meaning 'town'). Wether that means that (Old) Basque and Iberian are related, or merely an evidence of contact.
The fact that there is no language or language family (besides Iberian, perhaps) that appears to be related with it should tell you something: that it has developed independently for a very long time. For me, that is an indicator that Basque indeed developed in western Europe - that would explain how it is not related with the Uralic or the Caucasian language families.
I actually think that the conception R1b <> Basques has lead to a lot of very major misconceptions in the past (see: Iberian Glacial refuge).