It is VERY interesting that relativity and quantum mechanics can be derived from symmetries plus a sampling theorem. That says something fundamental about quantum mechanics. But Dick was not the first. Dick is very clever to do it all on his own, but is quite limited because he refuses to read any other work in his rather narrow field. He just got left behind.
There's a number of possibilities of what this might show, I tried to be creative and include as many of them as possible (so much for Dick's one interpretation of such results). Btw, sorry Aurino, I couldn't spare you:
1) There are laws to the universe that are driven by simple mathematical truths which symmetries and random sampling reflect in some fundamental manner.
2) The theories of relativity and quantum mechanics are somehow restricted by human ignorance, and symmetries and random sampling reflect the nature of our ignorance. However, there may be many ways to be ignorant and we just discovered the one path of perhaps many that just happens to match our observations.
3) Symmetries and fisher sampling are just approximations that emerge from the nature of the universe that happen to exhibit itself in the ways which are consistent with relavity theory and quantum mechanics. That is, all of these phenomena are related to something which is more fundamental than all of these observables. This underlying phenomena may not necessarily be 'laws' per se, it may only be regularities that we are more aware of which is seen in our prejudices in seeing symmetries and random sampling.
4) There are myriads of ways to derive our physical theories, with symmetry and fisher sampling assumptions are only the tip of the iceberg. Reality is such that there is many ways to derive our physical theories.
5) Mathematicians and physicists are just fooling themselves by selecting certain tricks used to come up with the physical theory itself. The reason this works is because the trick itself is what is important to theory creation. Even if the theory is true, there are just many ways to state the theory which happens to be trick-driven. Just by using the same tricks from a purely abstract approach, you can obtain the same theoretical results. The tricks are all arbitrary and were based on matching observations. Had our observations had been different, then physicists would have created different tricks and those tricks would have been used and Frieden or Dick would have created their models using the counterfact (hypothetical) tricks - thus being able to obtain the same counterfactual theories.
6) Theories are always to be seen as Ptolemic devices where we are constantly adjusting our theories to match observations. There is never any truth to our Ptolemic theories, just more continual adjustments. Likewise, we can create meta-Ptolemic theories that derive our Ptolemic theories, and this is just a matter of chance and creativity of the physicist. If looked at closely we would see the need to adjust the meta-Ptolemic theory to better match our Ptolemic theories, and adjust again those meta-Ptolemic theories once new Ptolemic theories are developed. This is just human creativity gone wild.
7) Mathematics and physics are just tautological games we play that conform to our human evolved prejudices. An extraterrestrial civilization would have a different kind of mathematics, with a different kind of physics, and their concepts may or may not be tautological or even logical by our conception.
I favor either (1) or (5). Which do you favor?