Rather unusually, the report you quoted did get one part right (although they failed to understand what it meant).
The key word is "should", because the song was written in a time and place in which it was widely considered unacceptable for a woman of good reputation to spend the night alone with a man who was not a close relative. She never says she wants to leave, because she doesn't. The format of the song is her singing about other people wanting her to leave, about how they are applying pressure on her to leave, about what they will think and say and him singing in reply about excuses she could give them to explain how her staying absolutely wasn't sexual (it was cold outside, there weren't any cabs, etc) and how she could place the responsibility on him (e.g. he was worried about her safety walking home at night). The song ends with her deciding to do what she wants to do, i.e. stay the night with him, and them singing in harmony.
She's not being pressured to stay - she's being pressured to leave. In their eagerness to find something, anything that they can fit into their tiny little warped view of the world, those critics have managed to completely reverse the meaning of the song. I'd bet dollars to donuts that most if not all of them have never heard it or read the lyrics or have any understanding of the cultural context of the song.
