Yes, that will link the Mountain Lion purchase to your Apple ID and this is happening because you upgraded to Mountain Lion through the app store with that AppleID.
What would be better is to get back to Lion that came with the system and does have this restriction.
Here is what you need to do to get rid of the Mountain Lion recovery partition and get back to Lion.
Use
this Apple utility with a 1GB (or larger) USB key to make a recovery USB key. Now option key boot to the USB key. Next start Disk Utility and click the drive brand name (like 1TB Seagate or whatever) and erase the entire disk. Quit Disk Utilty and shutdown.
Now remove the USB key and start the machine. This will take you to an EFI (firmware) based recovery that will get you back to Lion. Once the recovery window loads just click install OS, and Lion will be downloaded from Apple's servers and installed on the machine. This install will be linked to the serial number only and not your AppleID.