This seems made up to me. A bit too much like the movie Sneakers or something. Plus the resolution with the uncle being able to get the answer seemed too convenient. Is this a confirmed story?
If the number was such a big secret, how did his uncle, working at a random federal agency, find out what it is? Need to know should have kept it from the uncle, and goddamn common sense (and the threat of prosecution) should have prevented him from blabbing to his idiot phreaker nephew.
Edit: this guy watched too much X-Files as a kid. Replace the caller with Mulder and the uncle with A.D. Skinner, you've got something straight out of an episode.
The fact he included the area code and exchange in the story lends a certain amount of credibility to his story as he was essentially inviting phreakers to have their own fun.
I have similarly-exhilarating stories that I won't go into. But they gave my teen-aged self a great deal of fun touching the fabled "cloak and dagger" world. So, it's believable to me. Back in those days, there wasn't such an emphasis on domestic COMSEC. Anyone remember romulus at a certain US IC agency?