I'm having the exact same problem on a freshly installed copy of Windows 7 Home Premium (64-bit). I've run the CheckSUR tool as you suggested, and I've attached the zipped log file. Basically, it says everything is fine. However, the update refuses to install just as described by the OP.
Hello and welcome mikaly sorry you had to wait for so long - mate this update was to replace one - scroll down to the OS and click the MS at the end of the line https://technet.microsoft.com/en-us/.../ms15-056.aspx and see if that is listed in the update history. Now I am no expert but I would try uninstalling the old one and try again - IF that old update is still there.
I would certainly run these too
https://www.sevenforums.com/tutorials/1538-sfc-scannow-command-system-file-checker.html
https://www.sevenforums.com/tutorials/433-disk-check.html< if necessary include the /f and /r in the command line as per Option2
Your problem appears to be different -
Pleasefollow the WindowsUpdate Posting Instructions and postthe requested data
If thefile is too large (8MB compressed), remove the older CBSPersist cab files untilthe final file is below the limit - you can always post them separately afterzipping them. (the forum doesn't allow the upload of bare CAB files, for anumber of reasons)
Pleasealso post the C:\Windows\windowsudpate.log file
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