Hmm.
I don't think that this follows.
We don't even need to go back to ancient times. Take existing traditional healing cultures such as the Mexican curanderismo. To our eyes, this looks like a really strange mixture of herbalism, psychology and spiritualism. One might think indeed that the "theoretical basis" for such a healing system (e.g. evil spirits cause illness and they can be driven out with certain rituals) is groundless.
But why would that be a basis for thinking that the practitioners of curanderismo would or should have the same view as this? And if they did not, what would be fraudulent about their practices (given that many of them actually work. at least within a certain framework)?
When I talk about "a certain framework", I want to suggest that today we tend to take only a limited part of what "illness" is (i.e. its organic cause) and tend to focus on that. But actually, for the sufferer, the actual experience is much broader than simple symptoms. There are also problems of self-image and worth; and there are problems of how that person relates to the rest of their society. For example, and tragically, in some african cultures, the experience of having AIDS is not just confined to being ill (wasting, sickness etc). Sometimes, once people develop AIDS they are simply left in isolation: their family will have nothing to do with them, will not talk about them etc etc, as if they never existed.
Without a theory of organic illness (e.g. infection), surely it is natural for the entire pattern of experience taken together to be seen as "illness". That's why in a lot of folk medicine there's a lot of emphasis on "restoration" of the sufferer to their community (see e.g. the gospel stories of the lepers and possibly the woman with the bleeding): their state has led them to being classified as "being ill" - and the consequent social effects are indeed part of what the sufferer experiences - they are part of what it is to be "ill".
If you were an anthropologist in, say, South America, and observing traditional healing practices there, would you be inclined to say that the practitioners were "frauds"?