But a unique identifier doesn't necessarily identify a living person, particularly in isolation. It's just that it's frequently associated with a load of additional information that could eventually be used to identify someone (think advertising cookies when associated with a load of browsing data). So you can't escape from scope by saying you're using a unique ID rather than a name.

IP addresses are slightly different because that address can be used to identify the subscriber in certain cases (who in turn may or may not be an individual).