They might very well agree with that, yes. I think the article could in many ways be seen as an argument for fighting fire with fire. In other words, we should stop pretending that there are two equal "sides" in the conversation, and stop thinking of things in terms of belief. Because it's that word that's the problem right there. Really this whole idea is often a way to hide the ball. By couching being anti-vaccine as a "belief" rather than "ignorance," it no longer has to be defended rigorously. I think that's where the article is going, i.e. that we need to stop accepting the premise of the argument.
I don't think what you describe is actually the inevitabe result of the approach that I was suggesting. It's more about not accepting the premise, and not allowing someone to just say "I believe X" as a way to automatically foreclose all argument.