Can't you just send the PC back if it turns out it doesn't run linux?

I think you're right about a lot of things, even though I don't agree 100%. Individual points below

added value in buying from Tuxedo though as it gives peace of mind that Linux will run well

I think I see your point. All hardware that I've bought from PCS was absolutely compatible out-of-the-box, but then again, I knew what I want. (I've had two notebooks and one desktop computer from PCS if it matters, over the course of 5 years.) If I imagine myself completely not knowing anything about hardware and just buying some NVIDIA stuff, I could end up with hardware that ideologically doesn't mesh well with the "open" parts of Linux, and could be buggy and not working well on a practical aspect. The practical aspect was especially relevant years ago, now it smoothened out a little bit.

you cannot be fobbed off by Tuxedo on the basis of using an ‘unapproved’ operating system when you need support

Does PCS really do that in reality though? I've never heard of that. At the time that I was making my first purchase I was checking comments to their hardware, and people actually praised Linux support. They officially somewhat encourage it as well, as you can NOT pay 130 Euros for Windows by simply unselecting it during purchase. How can they afterwards make complaints that I don't have Windows? Do they really do that, can you reference anything to this claim?