They merely turned down the benefit that exact matches get - they didn't penalise anything. So to call anything an "emd penalty" is pretty unhelpful, as its not even close to what actually happened.
This was also a while back now - if the OP's client has been penalised recently, then it is clearly nothing to do with that update. If it was when that update happened, then both the OP and the seo company are failing to understand they haven't been penalised at all. An algorithm has just been tweaked to give exact match domains less benefit.
Agreed, they've turned down the EMD bonus, but that infamous "EMD" update did apply penalties to domains that tripped whatever filters they used... and it focused solely on EMDs. Call it what you like!