I'm going to start this time by saying I feel that quote, right there, best embodies the essence of postmodernism. Postmodernism isn't so much about political correctness and letting people "believe what they want to" or any such thing -- it's not about one person's truth being as good as anyone else's. Postmodernism asserts simply the following: the universe is made up of facts, but truth is in the mind only.
This statement does mean "there is no universal truth" -- but by that, it does not refute the existence of a single consistent physical universe, and the facts of which it is made. This argument is very closely linked to the tree falling in the forest -- more than likely, the air will be made to vibrate in any case. Only in the presence of perception does that vibration become what we truly call "sound." In the same way, postmodernism views truth (and the logic that applies to it) as things of the mind. Without interpretation, without the layers of perception and analysis we each posess (excepting, of course, a few truly dense people) fact never becomes truth.
We cannot take the logical "AND" of two facts, but we can take the logical "AND" of two truths. Logic is about truth, not fact. We are logical machines, bound by perception. We move about the universe sensing the facts around us, building a logical model of things in our minds, and moving forward with this new understanding. Perception without thought would not realize what it is, and thought without perception wouldn't go very far at all. Logic is a tool that needs material, and our perception feeds the machine. Before even "I think, therefore I am", there is "I sense." I would suggest for future reference, however, that we not define the idea of a conscious mind on this basis.
Drawing the line between fact and truth becomes difficult when we consider something like science: science aims to help us investigate our imaginary scenarios for applicability to the "real world" -- we have facts, methods of experimentation, and then we have ourselves and our imagination, hypotheses and theories. Scientific truth is theory: it is our tentative conclusion about the facts of the universe. Even the worst experiments, the most mismanaged projects, will turn up facts. How we use those facts is about perception and truth. And here's where the line gets a bit blurry: if you observe something happening, and then conclude something from this observation, where is the fact? Was the fact there before the initial observation, or was the fact actually in the observation itself, or does fact reside in the conclusion?
If we are a part of a greater, consistent physical universe, and our minds are linked to our bodies and therefore to the universe, then your belief about the world is part of the world itself. "Seeing truth" is a fact, and once noticed, is a truth as well.
Postmodernism, therefore, does say that there is no universal truth, but admits there may be universal fact. Postmodernism also admits that between fact and truth, there may be several levels of perception, and therefore several levels of fact and truth. The two are distinct, yet terribly related.
In the case of Dr. Jones' statement, we can observe that archeology may search for facts, but will likely find truth despite itself. Uncovering an object may seem like fact, but the moment we set eyes on the thing, we have truth, on some level.
Postmodernism further admits that our perceptions, our truths, may differ. They do not do so constantly: if nothing else, social elements will lead us to all say "blue" when we see the same color (the same fact) even if some of us actually (however this could be determined, if at all) sense the color differently. Absolute truth, therefore, would be the sum of all individual truths -- but how do we measure it, as compared to absolute fact? Could we take a single person and ask them to compare the two? Yes, but we would have a comparison between absolute truth and an individual truth only, and nothing more. Postmodernism therefore is the admission that we may see different truth from the same fact (or from several layers of perception, each involving fact and truth) ... but it does not require us to act on that understanding.
If a webpage is created with nobody to read it, does it make any sense? No. But that is obviously not the fate of this page, now is it?