Re: This has nothing to do with filters or illegal content..
... where 'anonymized' may or may not be true depending on:
(1) how well they understand and do anonymization
(2) who shows up with a secret warrant, court order, or friendly request
(3) who shows up with an envelope of cash for the custodian of the pre-anonymized data
(4) what resources an attacker can bring to bear for various high resource high/wide network access attacks