Note they didn't say it was just "not supported" but that it was _unable_ to run and was incompatible.
An example image of the error is shown here, http://ivanrf.com/en/nvidia-compatibility-issue-with-windows-10/ (nvidia-compatibility-windows-10-01-en.jpg).
Note Microsoft in their misleading error message give a handy link allowing you to purchase a new computer from them ... how, er, convenient.
The only thing is that the computer is completely able to run Windows 10. Running the upgrade using a Microsoft tool that was easily downloaded the computer ran, even without driver upgrade (albeit with reduced graphics) and after a simple graphics driver update (with an Nvidia.com downloaded installer) was fully working.
Clearly Microsoft lied in saying that the upgrade was impossible, their tool did it perfectly.
What should the response to this sort of fraud be? I wonder how many users like my father assumed they had to get a new computer to get Windows 10?