The nuclear wessels scene wasn't ad-libbed. It was filmed with a camera crew filming out the side door of a van on the side of the street. The cop in the scene was a real cop hired by the studio for security/safety and Nimoy decided to put him in the scene. All the passer-by’s where hired extras and weren't supposed speak, and they didn‘t. However, the "I think it's across the bay..." woman wasn't an extra she was just an ordinary person walking through who didn't know she walked into a movie. As the camera, though not quite hidden, wasn't really noticeable either. As far as she knew some Russian guy and black chick just asked her for directions. Nimoy liked her reaction and decided to use it, but they found out she wasn't an extra and had to run after her down the street to ask her for her permission and pay her.
This is the incorrect story that continues to go around although Layla Sarakalo, the woman in question, has given interviews explaining why she went to the shoot (her car had been impounded, she needed the money) and was hired as an extra, told not to speak, but ad-libbed a line anyway.
No one chased her down, etc. Check her listing on Wikipedia -- it should link to her interview.