Everyone was looking at their own shoes
"I can feel them looking"
The beam isn't an idea. It's a physical thing, heat in the face, a stiffness in the walk, an awareness of your arms that makes them hard to use. And a physical thing seems like evidence. If I can feel them looking, they must be looking. Nobody blushes at nothing.
Two findings bear on this. The first is from 1998, from Gilovich, Savitsky and Medvec again, on what they called the illusion of transparency. People believe their inner states leak out more than they do. In their studies, people telling lies overestimated how detectable the lies were, and people hiding disgust at a drink overestimated how visible the disgust was. An earlier book in this series used this finding for nerves at a party, and I'm using it here for the beam, because it's the same mechanism. What you feel from inside is vivid, and you assume it's showing at the same strength. It's showing at a fraction of it.
The second is from Warren Mansell and David Clark, published in 1999, who studied people high and low in social anxiety before and after giving a speech. Among their results was a pattern in the correlations, which was that the more anxious people seemed to be using their bodily sensations, the heart, the heat, to estimate how anxious they looked and how well they came across, and were wrong in both directions, overestimating the first and underestimating the second. This was in people at the anxious end, and I'll come back to what that end looks like in chapter 13. But the mechanism is ordinary. The body is being used as a mirror, and it's a bad one.
Once after the dentist I'd guess you've had a numb lip, and been sure it was hanging, visibly, in a way everyone could see, and checked in a window and found your face looked exactly as usual. The numbness was real. The hanging wasn't. The beam is like that. The feeling is genuine and comes with a body, and the thing it seems to report, a room of eyes, is a separate claim, and the way to test it is the way you'd test the lip, which is to look, and chapter 19 is that.