I'm astonished that what Santa says appears to deny the miscegeny that took place all through the 19th and early 20th centuries - the population of Wales doubled (at least!) during this period due to migration (from other parts of the UK) alone - and from experience (i.e. having been born and brought up in industrial south Wales, which is about as 'Welsh' as Tyneside) I can say that English, Scottish, Irish and a surprising number of Italian families seem to have moved lock, stock and barrel during that time (referencing people's anecdotal family histories, mind you) but are now culturally integrated to the extent that they're some of the most steadfast Welsh speakers in that part of the world.
I suppose that if you're looking for DNA markers, you'd be looking somewhere else (some rural backwater, maybe) and I bet you a pound to a penny that you'd get similar results if you looked in similar areas elsewhere in the UK...? ISTR a 'Meet the Ancestors' programme where old Julian had found a bronze age skull in Somerset (?) and on doing their usual facial reconstruction found that the face was the absolute spit of some guy who lived in that very village... Hmmm.