No, it is an argument against the position that we have a tight intellectual grip on the process of what goes on in the human body. It's also an argument against naive interventionism, eg. using antibiotics in less critical cases instead of waiting it out.
Though by that measure, it may become an argument in favor of homeopathy, for noncritical cases: homeopathy has no known (or conceivable, by the standards of the model we are using) side effects, and it appears to work as well as a "good" placebo. (I believe it essentially *is* placebo, possibly aided by the practitioner who spends more time with you than an average doctor and in a more relaxed environment -- with the caveat that we don't have a model for the placebo effect.)
So if you were to take two groups of people with cold/flu with viral and/or mild bacterial infections, it seems quite possible that those given homeopathic treatment (placebo) would fare better than those taking antibiotics (placebo plus gut flora disruption), which by the way used to be common for a number of people I know. It's possible even that gut flora disruption would impede recovery from illness.
And to make matters more complicated, by what measure would you know those people's health and how soon would you know it? Previous study of antibiotics on infections caused by flu probably didn't measure gut flora health for a year. And a person with a bad gut flora health for a year could be making other decisions in the course of the year that would affect their well-being differently than if they didn't have it. And so on. We know so little, and I don't think we can afford to be arrogant.