Only way we could get it to work at my office was to avoid the downloadable MSI. We had to extract the MSI and associated install files from the EXE here:
ftp://ftp.adobe.com/pub/adobe/reader/win/10.x/10.1.0/en_US/AdbeRdr1010_en_US.exe
Again, do not download the MSI.
Get the EXE and extract like so:
AdbeRdr1010_en_US.exe -nos_o"Reader10" -nos_ne
Funny, even though I specified "Reader10" it still prompted me for a directory. But if you don't put anything there I think it just throws everything into a temp directory and doesn't prompt you where to put the files.
So at this point you've got a directory but it's not your Admin Install Point. Go into wherever you extracted it and do the deeds (create the admin install point):
msiexec.exe /a AcroRead.msi
It'll prompt you for a directory.
So now you've got the AIP you made above. Go into THAT brand new AIP folder and then apply the patch:
msiexec.exe /a AcroRead.msi /p c:\FavoriteDirectoryToPutAllMyAdobeFiles\AdbeRdrUpd1013.msp
Copy that folder to a networked location (or whatever fancy GPO stuff one does) and point your GPO to AcroRead.msi and you're good to go. Only way we could do it at my office. I had it "replace" instead of "upgrade" all previous installations but I have no idea if that helped or not.
When we used any other MSI, downloaded or extracted, nothing worked.
Regardless, we've now got 10.1.3 deployed company-wide via GPO.
Hope this helps.