I'd caution that if there were other connecting passengers from the same inbound aircraft. and all of them made the flight, but for some reason he was the only one who missed it, then the OP will have a hard time convincing EK to refund the fee.

I'd bet this is the exact case, and therefore why the fee was levied. Their view is probably "How is it that 25 people from your flight made the connection but you did not?"