Depends where you start from, I would think- I often see a desire to derive things from the Latin! And it’s (ie a Latin derivation is) certainly an often overused derivation rather than underused.
I think it’s more just wanting to know where they are actually from, rather than having a dog in the race, as it were!
I share your interest and curiosity, Owain, and as a lover of languages, I follow my interest wherever the evidence leads me and even a bit beyond when conjecture has to take over. I beoieve that wishing to demonstrate that Welsh words descend from Latin would be as “unscientific” as wishing to show that they derive from any other language group. So in this enquiry we aim for objectivity (whatever that is).
You’ve referred a couple of times to the work of people in the Canolfan and Aberystwyth University and I know of no better or more rigorous sources on the origins of Welsh. (I’ll PM you what I know about the Aber people & work). There is, however, one hypothesis that I haven’t seen discussed which would allow for the viewpoints of both “camps”. Welsh and Latin share common roots in the Indo-European languages but an important factor in the current prevalence of Latin in Welsh, English and other contemporary European languages was the power and influence over several centuries of the Roman Empire. In other words Latin is not the origin of Latin-like words but the Romans provided the channel and means of concentration. Could we find common ground there? 
Oh, I wasn’t thinking in terms of “camps”!
Latin put a (huge/large/medium-size - all words which have no meanings without being further defined!) corpus of words into Welsh during those centuries. But there are (plenty of/some -see above!) words similar to Latin which come from Old Celtic and Indo-European without going through Latin first, as it were - all of which of course you know! Perhaps more in Welsh than in many other languages, as Celtic and Latin may have been (comparatively - see above!) similar, perhaps due to be splitting off from each other comparatively late, perhaps not. To such a degree it (from my purely hobby reading of the subject!) seems sometimes difficult for agreement to be reached on where they come from (Latin from Indo-European or Old Celtic from Indo-European) to a greater degree than say, in English.
In fact I have the impression (not that that means anything!) that Latin is usually the origin of Latin-like word in Welsh, but not always!
As usual, it’s just the details we are discussing! And not even necessarily disagreeing about!
Thanks for the pm - as interesting and entertaining as I would expect!