Hello,
as far as it it known right now, your suggestion is correct. But there is no one here who already can proove it by a present invoice. Any information obtained e.g. by the Cost Control (web or phone) is preliminary, the final answer is given by the invoice.
So my present conclusion is: be careful until you (or others) get an invoice where it is clear which content was included in the flatrate and which one not.
HTH, regards,
Dieter