Well, the article mentions antibiotic resistant infections like MRSA, (which by the way, fucking sucks) which are spread by skin to skin contact. The problem in this case is over prescription of antibiotics, but not quite in the way that you're getting at. The thing is, had we done what you're suggesting, then yes, we would now be better off. However, for certain strains of things, we are beyond that point. The use of antibiotics and sanitizers has created very, very strong strains of particularly nasty afflictions that people thought antibiotics had stamped out.
So yeah, for some stuff, getting down with the dirty is good for the immune system, but it also opens us up to exposure of antibiotic resistant shit. Unfortunately, antibiotics are in our food and a lot of kids aren't breastfed. Even those that are, get breast fed from women who have eaten stuff with antibiotics in it, at least in the developed world. What we really need is a strategy to strengthen human immune systems, not weaken things that challenge it.