Stresses can do all sorts of things, change gene expression, trigger proteins or breakdown products, etc, etc. All of those things can produce measurable changes.

[1]https://pubmed.ncbi.nlm.nih.gov/21392516/

The problem is that those are almost exactly the same kind of processes that theoretically could result in an "illness ray" leaving traces in the bloodstream.

A big problem here is probably that the US government haven't yet fully internalized how real PSTD and other stress related symptoms are, and is still treating it as if kind of "fake" especially when it comes to paying for treatments. so the people campaigning for getting the victims help is forced to push some sci-fy inspired illness ray theory.