I understood the point of broadcasting about the water situation on Midway was to trick the Japanese into passing that info on, using the designation AF, so they could verify that it was Midway. Was that not correct.
Exactly correct.
The film gave the impression that the broadcast of, "Our water distillation has broken down..!" had not been a very deliberate US ruse, specifically in order to get the AF location info from the Japanese.
That is correct. They bought the story.
It’s called a Canary Trap. Signals Intelligence Command was reading some of the Japanese codes, such as JN-25, and using radio traffic analysis. They were only reading about 20% of that. They could tell the the Imperial Fleet was going to attack somewhere, that the Japanese were calling AF and somewhere else, that they were calling AL. SIC had to figure out which was what.