2004? By the standards of genetics research, that's pretty practically outdated. Furthermore, the article claims how that "DNA origins of the Irish, Scots and Welsh" are in the Iberian penninsula (and that the ancestors of the "Celts" came there at the end of the last ice age, however, there's no mentioning of Haplogroup R1b, let alone of it's sub-clades. I shall de-refer you to this 2010 paper, which shows that Haplogroup R1b originated in Anatolia, and it's spread across Europe can be correlated with Neolothic farmers. Furthermore, if you look at R1b subclades (specifically subclades of RM-269), then you can see clearly that there's a considerable differences between Basques and the population of the Britain, even if they share the basic Haplogroup. Instead, they belong to different sub-clades of R1b.
You prove the OP's thesis nicely here.
According to your more modern and up to date paper (which only reinforces the ancient article I quoted earlier):
"
Other lineages also show evidence of European Neolithic expansion, hgE1b1b1 (E-M35) and hgJ, in particular [12]. Indeed, hgI is the only major lineage for which a Paleolithic origin is generally accepted, but it comprises only 18% of European Y chromosomes [13]. The Basques contain only 8%–20% of this lineage, but 75%–87% hgR1b1b2 (Table S1); our findings therefore challenge their traditional “Mesolithic relict” status, and in particular, their use as a proxy for a Paleolithic parental population in admixture modelling of European Y-chromosomal prehistory [22].
Other lineages also show evidence of European Neolithic expansion, hgE1b1b1 (E-M35) and hgJ, in particular [12]. Indeed, hgI is the only major lineage for which a Paleolithic origin is generally accepted, but it comprises only 18% of European Y chromosomes [13]. The Basques contain only 8%–20% of this lineage, but 75%–87% hgR1b1b2 (Table S1); our findings therefore challenge their traditional “Mesolithic relict” status, and in particular, their use as a proxy for a Paleolithic parental population in admixture modelling of European Y-chromosomal prehistory [22]."
So, according to this data the Basques may not be original Mesolithic dwellers but instead could be comprised mostly of the Neolithic group which started arriving about 10,000 years ago. Spreading into the islands around 6000 years ago. The Celts arrived in the islands 2500 years ago.
Indeed according to this data it seems even more likely the original inhabitants of the islands and the Basque were likely very closely related if not the same people.