Does she want ice cream? Answer: No, she doesn't. I added a not, so she's reversing the answer as Japanese people do.
The number of times I've been dumbstruck by this is larger than I'd like to admit, and I'm a coder.
Q: "Do you mind if I sit here?"
A1: "Not at all!"
A2: "Sure!"
Both are valid answers and mean the same thing, the person asking is welcome to sit there. This has always amused me.