As far as I could tell, that's not the case. After the install completes it asks to enter a new Apple ID (or a split Apple ID for iTunes and iCloud) and in my test install I entered my wife's ID instead of mine and the system was set up based on hers and there was no sign of anything to do with my ID.
I sold my iMac with Mountain Lion installed, in part because my children apparently absconded with my Leopard/Snow Leopard install discs. I'm sure they're somewhere in our house, but I have no idea where.
As a slightly OCD person, after selling it I had all sorts of concerns about security (such as: "did the disk utility on the LionDiskMaker install actually delete the drive?" despite taking hours to do its three passes)
And then, after the transaction, the question of whether the buyer would have access to my Apple ID. When installing you have the option not to set up an Apple ID (skip this step) so the computer, as sold, was set up without. Even if my ID is somehow linked to the Mountain Lion install, it's ultimately my email address -- not much to be done with that without authentication.
Yes, I had to think these things through thanks to some very unhealthy OCD paranoia
I'm sure I may have violated the EULA, but ultimately this installation of the operating system was bought and paid for and it's not going to be installed anywhere else.