Mine had a similar problem, but we went a different route than you posted. I'm actually surprised at the recommendation.
When it's red like that, it's a sign of infection. For mine, that meant antibiotics. My hedgie had to be put under and the vet had to go in and clean up the area - amongst the pus, she found a rather stringy quasi quill that we believe was the cause of all the mess. Had the vet not gone in to find it, we think the problem would have continued/worsened for my little one.
I've read of other cases of ingrown quills - not sure if they always required antibiotics... I'm hoping one of our hedgie gurus will chime in soon. But brushing the hedgie... that just doesn't sound right. You do not want to try and pop them like a pimple on your own either - that will just push the infection deeper into your little buddy.