I can say with pretty high confidence that there is not one MSC that handles mystery shopping for all Hilton properties. I have shopped various properties for a variety of different MSCs. Some I have not seen assignments for, and others have assignments posted from more than one MSC.
Like everything else, you just have to sign up for all companies, do good work and better assignments will become available to you. If you are looking to specifically gain access to a particular company offering Hilton shops, I would suspect you are either a Hilton Employee or have not signed up with enough MSCs. As a hotel shopper, it would be very dissicult to target one's shops just toward Hilton properties.