I just changed my MM companion for next year. Their account has the same mailing address as mine but I got a warning after entering their MP# that the addresses don't match and to certify that they meet the criteria outlined under the Terms and Conditions of the program. There was a handy URL link straight to the T&C's which clearly call out as #1 that they must reside at the same address.
I was given two options: I certify that they meet the T&Cs or I certify that they do not meet the T&Cs. I chose the first one and received an immediate response that my companion has been successfully changed. I do not know what would happen if I clicked the second option but I imagine an error saying that they must meet the T&Cs would appear and my companion wouldn't have been successfully changed.
So United is enforcing this to a degree. What happens if you lie and say they live at the same address but clearly they don't? I don't know.
-RM