Please see below.
He said she wasn't home on Tuesday nights.
- That's right. She's not.
- Yes [he was correct], she goes bowling.
- Yes [he was correct], usually, but this week she's home with a cold.
- No [she isn't home]. But she'll be here tomorrow night (Wednesday).
- No [he is wrong about that] - she bowls on Wednesdays, and is usually home on Tuesdays.
In those cases, a simple "yes" or "no" won't be enough information.