Since the company (WDL) flies to various destinations from LCY on behalf of CityFlyer (including EDI) it would appear that as far as they were concerned their paperwork and Flight Plan stipulated EDI as their destination. They therefore had no reason to question the SID received as it corresponded to the destination THEY were given by the company.
I disagree. The crew were expecting (and rostered) to fly to DUS so anything relating to EDI should have raised alarm bells in the pre-flight stage.