OK, I've figured it out now - they've used one of
these, a handheld XRF analyser. I work in a lab at UQ St Lucia; I didn't know somebody local had access to one of these.
Which does answer my previous question: XRF is a surface analytical technique; it won't tell you if the result is just surface contamination, or if the composition is like that all the way through.
That being said, there does not appear to be a lack of nickel in your "coppery" coin; the opposite, actually, with a Cu:Ni ratio of 2.8:1 rather than 3:1, there is a slight reduction in copper content; this would not account for the copper colour. I'd still conclude it was environmental damage. For a relatively pure metal, adding up all the ppm figures "should" give you pretty close to the theoretical 1 million parts per million; this coin falls far short, meaning there's an awful lot of undetectable elements (oxygen, carbon, nitrogen, chlorine, etc) sitting on the surface.
The "rimless" coin has the same problem, only worse: a distinct overabundance of nickel, with a ratio of 1.5:1, twice what it should be. What it doesn't really tell you is why: is there twice as much nickel as there should be, or is half of the copper missing? Copper being stripped from the surface selectively is far more probable than vice-versa, as copper is more electropositive than nickel. But I don't know if such "surface enrichment" is normal for well-circulated cupronickel alloy coins.
Here is where a couple of controls might have come in handy: a bright, mint-fresh coin, and a well-worn but otherwise normal coin.
As for the trace levels of other stuff (manganese, silver, mercury, etc), that's pretty much par for the course with raw metals that are sourced as cheaply as possible. It's too expensive to remove those last few fractions-of-a-percent of contaminants, if you don't really need to do so. It doesn't really mean too much, except that such trace-level detection can in theory be used to "fingerprint" the metal and trace it back to its origin. I've read about analytical work done on ancient coins that demonstrate the likelihood that certain ancient coins were likely to have had their metal mined from a certain place, as opposed to another place.
Don't say "infinitely" when you mean "very"; otherwise, you'll have no word left when you want to talk about something really infinite. - C. S. Lewis