Sorry about that! and sorry I missed your message.
EMBA is an interesting animal. It is for-profit and the AdCom is not really an adcom, but more of a curator team who allows customers access to the product. If this makes sense. Anyway, what this means is that you can and should call them up, the AdCom that is. They will be happy to spend an hour with you and go over your profile, concerns, and help you save time if you are not a fit or try to convince you to apply if there is. Many have found EMBA teams to be very helpful in giving straight answers and not being vague.... There are a few competitive EMBA's, Haas and Wharton are the 2 that come to mind but most of the others such as Kellogg and Booth are quite friendly and open to a diverse group of folks. I wonder if the advice you received was directed towards FT MBA? There are no many EMBA consultants. Could they have been confused?
Anyway, about the advice you received, I totally understand getting a pretty bad aftertaste but I would not dismiss it. There is no reason for a consultant to lowball you, and if anything, they are more motivated to paint a rosy picture that you can get in anywhere with their help. Not doing the latter is not helping them. Obviously I am not sure why they would say this but I would use it as a datapoint and be straightforward with the EMBA Adcom - do you see weaknesses in my profile. I would say you got a consultation and you were told XYZ, etc. Let them try to sell their program to you... which they will