I'd say she's wrong (the teacher, not your DD)!
The EBC (not sure that that is the correct chosen moniker!) and the EBacc are 2 different things, surely?
EBC is the new 'O' level style exams, first due to be sat in 2017 (I think!) when today's Y7's are in Y11.
We've been clearly told that the new EBCs will only apply to certain core subjects initially (Maths, English and is it Science? Not sure) so today's Y7s will be the first sitters, but only in these subjects. They'll do GCSEs in the others for teh time being.
The EBacc, as I'm sure you know, is a (crude) measure of a secondary's performance, 5 GCSE passes in Eng, Maths, Science, a MFL and a Humanity, either Geog or History wheeled in 2 years ago.