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Banks don't need a SEPA mandate to allow a direct debit?

The SEPA mandate is between the parties in the transaction. While banks require their existence, it is usually not shared with the banks involved.

So only a creditor ID is needed if someone has a set of IBANs and then things will be processed?

A creditor ID and a direct debit agreement with some bank, yes. After you have those, (usually) the banks won't verify individual transactions.