Children who see their parents react to every negative thing they do assume the child can set the agenda. Ignoring the misbehavior allows the parent to communicate to the child that the parent is in control of the relationship and the parent will deal with the situation when the parent is ready to deal with it, not the child.
To some children, no attention is worse than negative attention. Ignoring Brian is its own form of punishment.
Secondly, the mother and child were in a public setting and it's not uncommon for some liberal do-gooder to report to CPS a woman using physical discipline against her child. She may have been restraining her anger until such time as she and Brian were out of sight. Once alone (home or possibly a bathroom stall) Brian will get "delayed justice".
Just because the author didn't get the satisfaction of seeing a swift slap to the butt doesn't mean it didn't eventually happen. And discipline, even delayed discipline, is needed for this sort of situation. Otherwise, you'll be raising little Bill Clintons and James Carvilles.