I finally found this one. It's "Phreak Encounter" (1986) by Roger MacBride Allen, published (only) in Analog, May 1986.
You can get anything from the BBS as long as you give it a fact:
YOUR FRIENDLY NEIGHBORS BID YOU WELCOME. FOLLOWING IS A LIST OF SERVICES AND PROGRAMS AVAILABLE ON THIS BOARD. THE RULES OF THIS BOARD ARE SIMPLE. FOR EVERY USE OF A FRIENDLY NEIGHBORS SERVICE, YOU MUST FIRST TELL US A NEW AND INTERESTING FACT. ONE SERVICE, ONE FACT. WE HAVE PLENTY OF PHONE LINES—NO TIME LIMIT ON USE. ENJOY!!!
The BBS is using an unassigned exchange not an area code:
"Gimme a customer name and address on this number." He punched in the Friendly Neighbors number.
"That Maryland? Area code 301?"
"Cliff, where you been? That exchange isn't even hooked up!"
They don't have to do any fancy investigation to find the address; the BBS tells them. But when they get there:
That melted green cable came through the wall over the door, and led to a—thing. Barringer didn't know what to call it. It was a boxy shape, about four feet square, of the same dark green color as the cable. It looked half-melted, too, its shape softened, rounded, droopy.
Another green cable led to a device Barringer and Zamoiski both recognized instantly.
There are certain machines that must be certain shapes if they are to work. A square wheel cannot roll, a lever must be long and thin to do any good, a knife
must have a cutting edge.
Zamoiski gasped as Barringer shone the light on a twelve-foot diameter, bright-green, well-polished, very handsome parabolic dish antenna.
Zamoiski tells the BBS the fact that it's not from Earth:
Zamoiski reached for the keyboard. "They aren't spying. Just looking around. And that door wasn't locked. They must be expecting us. Lemme get their attention.” The sysop of this board is an extraterrestrial, he typed.
They are promoted to the next level:
HELLO, NEIGHBOR. YOU ARE NO LONGER LIMITED TO THE SMALLER BEGINNER'S BOARD, YOU HAVE JUST QUALIFIED FOR PROVISIONAL MEMBERSHIP IN THE MAIN BULLETIN BOARD SYSTEM. DO YOU WISH TO JOIN?
"Damn straight I do," Zamoiski said. Yes, he typed.
THE RULES OF THE BOARD ARE SIMPLE. TELL US ABOUT YOU. AND WE'LL TELL YOU ABOUT US. ANSWER ONE OF OUR QUESTIONS. AND GAIN ACCESS TO ONE SERVICE.
The operators of the board aren't concerned with deep secrets:
And Zamoiski was just crazy enough to show the Neighbors how he had patched into the Lawrence Livermore Lab computer that time, in exchange for an hour of gaming.
What would they want to know?
The screen cleared. Another pause. And then, on the screen—
TELL US MORE ABOUT TED WILLIAMS.
Barringer sighed in relief. "I think," he said, "it's going to be all right."