Windows DirectX install error "SetupInstallFromInfSection"

Freshly installed Win10 – after games didn't start because of seemingly DirectX errors, I tried to install it (both offline and web installer). All failed with this log message:

[11/03/17 10:38:31] module: dxupdate(Nov 19 2010), file: dxupdate.cpp, line: 2056, function: ExecuteInf

Failed API: SetupInstallFromInfSection()
Error: (123) – The filename, directory name, or volume label syntax is incorrect.

Unable to install C:\Users\*******\AppData\Local\Temp\DX9F05.tmp\XACT2_1_x86.inf:[x64_install]. The file may be damaged.

I tried to access the file (the temp files aren't deleted until Ok is clicked on the error) and they are there and available.

Windows's DxDiag doesn't report any error, shows DX12 installed. I tried SFC and DISM but they didn't report any error.
What could be the problem?