Part of the essence of science is that specific conditions can be deliberately created and tested. The ability to deliberately create the test conditions is essential in science, because it provides the only sure means of separating out cause and effect.
Suppose I through a bunch of different stones, marbles, and other such objects into a jar and shake it; some of the items settle out to the bottom. Mere examination of what pieces do or do not settle out would not suffice to ascertain what causes some items to sink deeper than others. One might be able to make some informed guesses, but to really show what properties have what effect, it would be necessary to run the experiment with items that were identical except for specific chosen properties. Mere observation could lead to erroneous results if, e.g., smaller items happened to be generally either denser or lighter than larger ones (and odds are pretty good they'd be one or the other).
Further, there's another problem with trying to 'predict the past': the fact that something could have come about via a certain mechanism doesn't mean that it actually did. People doing forensic studies on things that fail often have this problem. Even in closed systems, it's often not possible to tell with certainty how a particular bad situation came about. And in open systems, it's generally impossible. Given that the known universe is an open system, it's not really possible to identify all the major factors that affected events millions of years ago.
...One might be able to make some informed guesses, but to really show what properties have what effect, it would be necessary to run the experiment with items that were identical except for specific chosen properties. Mere observation could lead to erroneous results if, e.g., smaller items happened to be generally either denser or lighter than larger ones (and odds are pretty good they'd be one or the other). ...
Yes, but another way to eliminate such sampling error is to take many samples from as different contexts as possible.
A good example is in radiometric dating. Any single rock sample could indeed be subjected to water, heat, etc. during the years it's been in the ground, and that contamination could throw off the implied dates. But when you take several samples, from different areas, and examine different radioactive elements for their decay ratios, you can distinguish between contaminated results and valid ones. Because different chemical elements will react to water or heat or other stresses differently, and samples from the next hill over were probably subjected to different levels of stresses than the first hill. This is why the common creationist criticism of radiometric dating fails.
So, sure, paleontology is, pedantically speaking, an indirect science, in that they aren't able to do a medical exam of the living ancient animals like they can with live animals. But at some point a big enough pile of circumstantial evidence is just as good as a collection of direct evidence. Heck, even in your example of directly shaking the stones, you have error & imprecision & sampling error, so direct evidence isn't logically privileged either.