Miss Brill did not interfere with the people in the park because she enjoyed listening to them and watching them more than interacting with them.

Miss Brill is an older woman who lives a solitary life.  One of her favorite things to do is go and sit in a park and people-watch.

Miss Brill likes to watch people, but she also likes to listen.  She sits in her own “special seat” in the park, and likes it when the people talk, and “always looked forward to the conversation.”  She wears a fur that she enjoys putting in her lap and stroking.

She had become really quite expert, she thought, at listening as though she didn't listen, at sitting in other people's lives just for a minute while they talked round her. 

Miss Brill considers herself a play she likes to watch, and she realizes that she is a part of the play.  She always comes to sit on that park bench, just as the band always plays.  If she was not there, someone would be sure to notice her.  She still does not interact physically, but in her mind she is interacting with them just by being there.

Oh, how fascinating it was! How she enjoyed it! How she loved sitting here, watching it all! It was like a play. It was exactly like a play.

"Miss Brill" is a story about the isolation we all face in society.  Miss Brill really does not have anyone to interact with.  She therefore creates a rich fantasy of interaction, and imagines herself as part of the larger picture.