Sounds like a problem with your correspondent’s Live ID login. He may have used a different name when creating the account (an alias) and then forgot about it.
Be sure to check the email address that the invite came from.
I sent an invitation from my hotmail account to my work account just now and everything worked as expected.
I'll ask him to re-invite, and confirm his Live ID login beforehand.
Nothing against MS, but their concept of 'customer support' and mine are simply galazies apart. Plus, I speak coherent English, which can not be said of some considerable portion of their CS agents.