We are probably ALL guilty of unwittingly passing various nasties around.
You don't have to display symptoms (or even to succumb) to carry and spread many viruses and diseases, so the argument that having "sniffles" is going to infect everybody else just doesn't hold water. In fact, contagion is probably most risk-bearing pre-presentation (that is, before it's obvious....)
Besides, if everyone who had "sniffles" or just generally didn't feel 100% didn't bother to come to work, the whole operation would grind to a halt.