How much of the conclusions drawn from these investigative techniques are justified entirely by analytic chemistry, and how much goes beyond that? Using an example from a related article, there's a substantial difference between being able to say what's the chemical element composition of a particular bullet and being able to identify the particular manufacturing facility and batch it came from. The latter relies on a whole lot of assumptions about the ammunition industry.

>what would that even mean?

I gave an example at the top level comment. Apply the test (blind) to known innocent samples too, and see whether it implicates them.