Actually, that is a good news in the sense that we now know how to qualify only for CEC. The questions in EE simply asks if you have a job offer, and then asks separately about LMIA. It does not ask if you have a VALID job offer, as in supported by LMIA.
I didn't know about the FAQ answer mentioned above, but yeah seeing that answer clarifies everything. However, what do people who already have ITA do now? I would suggest everyone who got FSW ITA, when they qualified for CEC as well, to send an email to CIC, asking them to revise the ITAs to CEC.