She was also married to jazz musician Artie Shaw. He told the story about doing some USO tour and a soldier came up to shake his hand. "Wow, I shook the hand that touched Ava Gardner's tit." Shaw (who had a Sinatra-esque temper) said they had to hold him back from hitting the guy.
The Code was a lot different in those days. Brawling was encouraged and any sexual comment or innuendo about a guy's "girl" or wife would start a fight.
In that context, Shaw's reaction isn't as strange as it appears today and the soldier's comment is socially provocative and weird.