Well "reality" is all that / who exists; so from one perspective if "man's view of reality" changes; that bit of reality that describes "man's view", changes.
But James Burke sounds like he is saying that reality is whatever you think it is. That does not seem right; except it could be if one was perfectly honest? Christianity teaches "as you measure, so you are measured; knock and the door will be opened to you; if you had faith as a grain of mustard seed you could say "move" to this mountain and it would move"; but how literally do we understand this?
My brother points out that the ancients who believed in, say "Zeus" to use Dr. Dick's example; didn't have Jumbo jets. In "what is this thing called science?" R.F. Chalmers finds that progress in science may be seen as increasing freedom.
If you were playing a Chess game but could only see a few squares at any time and did not know the rules or the size of the board; but were limited to the actual board and rules; any theory you might have, about the game, might be more limiting than if you knew what the game really was.
So your trial and error and thinking-based figuring-out as you went along of: "what is this game you are playing" would be characterised by increasing freedom in moving your pieces as you figured out the minimum constraints on the game.
Progress in science might be like that. So how could reality be changed by knowledge? It might be that "a muddled and overly-restricted view of reality" might be changed by knowledge.
In the Chess game example where you can not see more than a small part of the board and know few rules; your freedom to play increases as you navigate out of say confusion-based restrictions on the game and rules.
But where I disagree with Dr. Dick and James Burke: if they are saying there is no fixed reality; I think there is a definite reality but I acknowledge that if one is "living at the edge" of that reality then that reality is much less restrictive than people might think.
Imagine if you had a consciousness where you could see many possibilities of alternative pathways of people achieving particular goals; as compared with being aware of only a few paths? The Kingdom of Heaven has been described as like a mustard seed that grows to a great tree, and the birds of the air find nesting space in its branches.
If we were more conscious of each other we would surely clash less and see more ways of being in harmony?
The Chess model fits your idea of "diferent phases of knowledge with respect to the question of the validity of such knowledge"; ultimately if one reaches the full knowledge state then one knows the size of the board and all the pieces and the rules and can play with the freedom that gives.
But in life; the "game" seems to involve a direct harmony with our Creator; so the idea of "Eternal life" seems to suggest that we and the universe are being created together.