After much prompting I decided to update to PhpStorm 2016.2. Maybe one day I’ll find the real cause of the messages I get that tell me files don’t exist when they do. Meanwhile, I realised that I needed to improve my problem reporting from a file that had been marked as deprecated. Even though it produced a proper WordPress message to say it was deprecated and also produced a debug_backtrace, when accidentally loaded in PHPUnit the file didn’t actually tell me who it was. The output didn’t have any useful identifying marks.
More recently I upgraded to 2016.3.2.