The drivers WTWF is complaining about don't work on WindowsRT, 8.1 or not. The whole "Windows 8.1" thing is a red herring. The reason the drivers don't work on WindowsRT is because only Microsoft signed drivers will load on WindowsRT. They didn't load on WindowsRT with 8 and they won't load on WindowsRT with 8.1.
And no, the drivers WTWF is talking about aren't Microsoft signed drivers because Microsoft doesn't make NICs. They are probsbly Broadcom/Verisign signed, not Microsoft/Microsoft or Broadcom/Microsoft signed, hence why they don't load on the MicrosoftPad.
As you can see from the screenshot above, the drivers are signed by Microsoft. And I'm using them on Windows RT 8.0 right now.
I suspect the ASIX/Microsoft story goes like this:
Microsoft signed these drivers for ASIX to perform in-house RT testing.
ASIX, in confusion, put these up for download.
Microsoft learned of this and requested pull down, given they're not certified for use on Windows RT.