I have come across the term 'inaccurate knowledge' - and explanations of it - in the work of Owen Barfield; and it has been a great excitement to see something which I had felt, and even written about, so clearly set-out.
Barfield makes the point that before the modern era (before approx the 17th century) it was implicitly understood that knowledge could be inaccurate and still be knowledge; but that since then, and increasingly, knowledge has been equated with accuracy to the extent that:
1. That which is accurate is assumed to be knowledge, and
2. What is not accurate is assumed not to be knowledge at all.
This combination of assumptions is a thing I have struggled against for some twenty years in addressing the use of statistics in medicine (i.e. epidemiology, medical research, 'evidence-based' medicine and so forth).
Barfield locates this phenomenon in historical terms as something that was a more-or-less-inevitable transitional phase in the development of human consciousness - but a phase that ought to have been (but so far has not been) transitional.
Before modernity, legitimate knowledge included 'inaccurate knowledge' - that is knowledge which was true, but imprecise - and, as a consequence, included knowledge of that which was 'supersensible' - the 'invisible world' of things that are non-material, imperceptible to the senses.
The defect of the kind of accurate knowledge that has been associated with mainstream science and research is therefore that it is (by assumption) positivistic: that is, confined to the material world, to that which can be perceived by the senses (included by the technologically assisted senses).
Consequently, we get the modern situation variously termed positivism/ materialism/ reductionism - of the human consciousness alienated, solipsistic, utterly cut-off-from the rest of reality. On the one hand we have accurate knowledge of the material world, on the other hand we deny any possibility of knowledge of the supersensible world, and indeed deny (by assumption, that is by metaphysical assumption) the reality of the supersensible world.
And the thing that this modern positivism should-have transitioned into is an accurate form of 'supersensible' knowledge - that is to say, knowledge which is potentially accurate and also includes the supersensible. In a nutshell, the idea is that the supersensible, non-material world is perceptible to the 'imagination' - which turns out to be potentially a kind of sensory organ for detecting the supersensible.
However, the ability to use the imagination potentially-accurately to perceive the immaterial does not come naturally or spontaneously to modern Man - presumably because of the antipathetic social milieu.
The missing link which prevents this transition is that we have so deeply internalized the metaphysics of modernity (the assumptions which deny the reality of the supersensible) that we have become unable to think and behave in the supersensible world - we have become blocked from progression by our ingrained metaphysical habits.
So, after understanding in a theoretical fashion that there is more to the world than the material and that the imagination is potentially the mechanism by which we might appreciate the supersensible world in a way that is clear, alert, purposive hence potentially accurate - then we can recognize that this is a mental ability which is rare, and difficult of attainment.
It is one thing to know what we ought to do, and it is another thing to do it. But actually doing it, in thought and behaviour, is what we ought to do.
And that is our task.