Both of them - the Egyptians and the Basrawis - are able to communicate without issue using Modern Standard Arabic, and worse comes to worse, the Basrawis wouldn't have much problem to emulate the Egyptian accent (almost all of the TV dramas, films, actors and music is in a Lebanese and Egyptian accent, so pretty much every Iraqi living in Iraq would have no issue with it). It would never reach a point where they can't communicate with each other.

The paragraph itself seems slightly misleading or enhanced for dramatic effect. If this situation did actually take place as claimed, it's likely that the locals were intentionally trying to confuse the interpreter.