This is a fascinating rabbit-hole for people like me who enjoy this sort of thing!
I looked at a few big car rental companies' websites and they all say that if you are renting in the UK with a UK licence you need a DVLA check code. None of them says, in so many words, "If you are renting outside the UK with a UK licence you don't need this code", but I think it's reasonable to take that as read.
The exception is Hertz, which has this strange paragraph at https://www.hertz.co.uk/rentacar/reservation/policy/policy-detail/enGB/LHRT50/LICENSE:
"When renting in the UK, Angola, Bahrain, Balearics, Botswana, Canaries, Croatia, Namibia, Oman, Portugal, South Africa, Sweden and Tunisia, all drivers with a UK licence will need to provide evidence of any driving endorsements. This also applies if you have a paper licence that was issued before 1998."
It then goes on to describe how to prove that you do/don't have endorsements, via the DVLA check code.
That's a very strange list of "countries" (and of course the Balearics and Canaries aren't countries, they're part of Spain, and the rest of Spain isn't mentioned). Maybe this is based on agreements between Hertz and its local franchisees in those areas.
If you're renting with a local company in Spain, I would be amazed if they have even heard of the DVLA check code. They rent cars to people from 50+ countries and presumably want to have a single check-in procedure for all of them, give or take perhaps an International Driving Permit (although these days almost every country issues credit card-sized licences that meet the requirements of the international conventions and an IDP is no longer needed). I would be surprised if they have gone to the bother of training their staff in how to read a certificate from the driving licence authorities of Liechtenstein to the effect that the holder has X number of penalty points, even if Liechtenstein were to issue such certificates. It's noticeable that none of the big chains seem to ask for that kind of proof in the UK from holders of non-UK licences.
So I think that bit about what companies "may" ask for is mostly arse-covering by the people writing the articles. If people are being asked for DVLA checks in Spain I imagine Simon Calder would have written about it. (But maybe he has!)