Dumb and dumber

There are lots of situations where its better to lack information

• a sports fan who taped a game for later viewing, and actively resists learning the score
• a couple choosing not to learn the sex of their unborn baby
• a reader who makes her friends promise to not 'ruin the ending' of the book
• manuscript reviewers not knowing the identities of the authors
• juries not knowing the past criminal record of the accused 

So there is plenty of precedent for a service provider deciding not to bear the responsibility (and risk) of holding PII.