Finally, when I got to work... I transferred one of these EXE files from the phone to my computer and picked it apart. It looks like the response AT&T sends you when your account has become persona non grata, like for instance your prepay data credit ran out.
I have no idea what response the browser received from AT&T to cause this redirect to be downloaded as a file. Perhaps there were double headers. But where did the filename come from? Well, I restarted the phone and now the problem is gone. All very odd.