It is exceedingly difficult to understand the various presocratic philosophers from a few extant fragments or quotations preserved in later philosophic writings. Moreover, as a group, they represented a transition from a cosmological and religious explanation to a philosophic and scientific (i.e., natural) view of the world, and thus their writings contained elements of both horizons.
Since the fragments are all we have, they will have to do. I suppose the question is what it is we can understand from the data we have. The truth may be utterly different, but that is somewhat unlikely. We always have to make inferences from the available data, and, of course, as Quine tells us, all theories are underdetermined by the data however much data we have. I agree that the presocratics represent the transition from supernaturalism to naturalism. It is worth noting that Socrates himself held that we knew too little about the natural world to be able to say anything useful about it, so that philosophical investigation ought to be into what we do have information about, namely ourselves and Man himself, and what we ought to do. That is, investigate morality.