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Their own privacy most likely. Don't want to reveal the techniques used to identify the accounts they ban, so the scammers can't learn from it.

Many companies have a policy of not explaining how their abuse detection works because the information aids abusers.

The stuff about privacy is just nonsense from a clueless support person.

For privacy reasons implies either what you are suggesting or that they are contacting Discord from an email address not affiliated with the account in question.

The user specifically said they were using the email address associated with the account.