I have seen this before where Malwarebytes will not update. In the past I could burn a CD from a good computer, delete the files in the Anti-malware folder, copy the files from the CD to there and it would run. This malware locks the entire Malwarebytes folder to prevent this action. I have ran all of the utilities on your site, rkill, Microsofts malware remover, SuperAntiSpyware, Spybot Search and Destroy and Symantec's deep scan and nothing finds any problems. This is consistent with what I have seen in the past, none of the other products even look for this type of malware, only you product detects them.
The attached diagnostic text file is all I could capture from running the MBAM support tool, it would create the file and then the file would be deleted. This is a devious little bug!
I can allow you to attach to my computer and run any thing you wish. I also have another computer at my sisters which has this same issue.
Diagnostic.txt
JRT.txt