The EA had no agreement with the OP, written or oral, to pay any fee. In the absence of such agreement, it would have been perfectly reasonable to assume the prospective buyer was paying. As Murt10 has pointed out, this would not be at all unusual. The EA is obvously trying to have it both ways. How could the EA sue to enforce a non-existent contract?
The analogy with a window cleaner is weak. If someone called asking if I wanted my windows cleaned, it would be obvious they weren't acting for some third party who thought my windows looked a bit dirty. The first thing I would ask (assuming I might want them cleaned) is "How much?"