The version of the Lena Horne story I heard was that a mouse fell out of the flies and landed near her on stage. She said 'I've worked with bigger rats than that' and threw it offstage.
I have to admit your version sounds more likely. I was working at the Nederlander, where it supposedly happened, when I heard it, and at the time that theater was a real dump. I could easily imagine a dead mouse falling out of the flies.