I'm glad we're more on the same page than I initially thought.
I do agree that at the time the song would be understood to be conveying a woman who wants to spend the night but feels socially obliged to say she doesn't.
I think where we diverge, though, is in whether or not the song is depicting an accurate representation of how women responded to these social norms.
In this song, we are presented with two people who are not being observed by anyone else, so her need to say "no" only for appearances' sake is questionable.
If this song had been written with an equally likely scenario for the times, where he instead assures her that her secrets are safe with him, then the song might have been considered scandalous.
Instead, this song posits that it's intrinsic to women's nature to use the word "no" as a negotiating tactic, whether in a private or public setting. Did women at the time agree with that, or did men at the time have more say in how that gets shown in the media?