You seem to feel there is something about that one machine that is different from the others. Have you compared the machines for software, such as anti-virus. The update seems to address a certain type of user that might be able to compromise the system. Are your user settings the same for all machines.
The error 8007371b seems to be:
ERROR_SXS_TRANSACTION_CLOSURE_INCOMPLETE
One or more required members of the transaction are not present.
The update contains 10 packages. On my system, packages 2,3 and 9 were installed. There is a possibility something is missing or wrong with your packages or the ability to access them is restricted.
The Side by Side (sxs) reference may be involved. There have been some postings lately about SxS errors but all I can do is give you
this link to a college site and let you see if anything makes sense.
If you want to send me the files mentioned, in their entirety, plus the
CBS.log in the Windows\Logs\CBS, you might be able to do that in a private message, or I can pass a e-mail address. If you do so, I cannot guarantee I will find the problem, but it won't hurt to look. Probably not a good idea to attach a large text file such as these might be.
Beyond this, I don't know what else to suggest. The fix you did will rename the SoftwareDistribution folder and perhaps a .cab file. If you have not run the
Link Removed tool, you might look at it. The fact the other updates worked and this one does not, would seem to indicate something broke on your system, or this specific update is having some type of conflict with your one system.