I read about their alien abduction case years ago. I remember that they did not remember the incident until problems Barney was having prompted him to undergo hypnosis. Then both of them went under hypnosis, each filling in pieces of the story, including a star map which Betty drew. I think they lived in New Hampshire.
Because star distances were only poorly known at the time, investigators could not tell where these stars were in our own sky. Only later, when an updated star catalog came out did they figure that the two main stars were two Solar-type stars named Zeta-1 and Zeta-2 Reticulae, closer to each other than Alpha Centauri is to our sun.