Yes it does. It's possible to identify a person with that information, so it's "personally identifiable information". Just like having a name you once gave is "personally identifiable information" even though some people can lie, others can change their names, and still others share names.
Which is stupid. People shouldn't share names. It's not like food, which can be divided without disappearing.
The only solution to this problem is forced deathmatches.
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