It's a reference to hanging, which was certainly less common for women than men, but still happened with some frequency. The line is mainly a clever way to say not to believe a bad woman unless she is stating the obvious (being up on a scaffold and condemned to die, she would not be allowed to come off of the scaffold). It also suggests a favored ending for bad women in the eyes of the singer.

Watson got the song from a longtime collaborator, Clarence Ashley, who sings a similar verse:

Now boys don’t believe what a young girl tells you

Let her eyes be blue or brown

Unless she’s on some scaffold high

Saying, “Boys, I can’t come down”

Notice that Waton changes "young girl" to "bad woman." This makes the fate of the woman being hanged more deserved, since she was presumably "bad" in some moral and criminal way. Ashley's version is more violent and misogynistic, since "young girl" carries no connotations of being deserving of a hanging. That version is suggesting that young girls in general are not to be believed and perhaps should be hung, as opposed to just the "bad women."

Killing women is a pretty popular thing to do in American folk music, and happens to women who seem to "deserve it" by doing someone wrong and to women who don't. There's a whole genre of "murder ballads" like Tom Dooley, Little Sadie, and Omie Wise that feature the death of women at the hands of their lovers. Songs about killing women who have done the protagonist wrong were popular in the blues, with songs like James Alley Blues, 44 Blues, and Single Tree Blues.

So the images of hanging and not trusting women are completely in keeping with the way women were depicted in many similar songs across traditional American genres, and the line is essentially a macabre joke.