As you say the food evidence seems jumbled. It has been claimed that the fish was prepared in a way that the natives don't and that they do not eat reef fish. Yet fish traps would point to the catching of reef fish?
AT the risk of appearing silly (a risk I take and suffer from often

) I can say that I have no idea how one could differentiate jumbled fish bones to tell by whom they were cooked and eaten. Or even differentiate fish species - on all the digs I worked where animal bones and other fauna were present we had people who were trained in that to do the analysis. An archaeologist is at times nothing more than a ditch digger with lots of letters after their names
However given the previously noted concern felt by the Polynesians about eating reef fish because of that poison
ciguatera (
http://en.wikipedia.org/wiki/Ciguatera ) they ingested from reef flora I might suggest that if a fire place was found which had around it fish bones of reef fish then you might make a informed guess that this could be the remains of a European's meal. Now in the Bushnell Report (1st Part page 3)
http://tighar.org/aw/mediawiki/images/5/52/Bushnell_Part_1.pdf there is an interesting sentence which reads
"It is advisable at all islands with lagoon access to the sea to eschew the Red Snapper and small reef fish".
Now is this is a reference to that poison they pick up? quite probably as that report is a pretty good study of the islander habits. Red Snapper is a popular and fine tasting fish while snapper of various types world wide are extremely popular. In fact I would suggest that anyone who was a castaway on an island like Nikumaroro and familiar with eating fish would happily seek out Red Snapper. They are a largish fish and unlike small reef fish would provide a good meal in one catch. However if that person did not know that the fish could carry
ciguatera from the reef flora then they would also poison themselves, so theoretically a camp site with a small midden that contained Red Snapper bones, or any reef fish for that matter, might just be that of a European.
Again that is no more than a simple conjecture based on some known information but it is far from being any real working explanation to differentiate midden contents by the ethnicity of the person who produced some of the midden's contents. There is nothing to say that a Nikumaroroan couldn't have eaten the same fish and not got ill and also
ciguatera doesn't seem to be present at all times so in the fish food chain some fish might simply not eat a contaminated herbivorous fish - it seems to be a bit of a lottery. Which is all to say I ain't no expert on this
Edit: And yes the presence of fish traps inside the lagoon either makes a lie of the supposed Nikumaroroan reluctance to eat reef fish, or the fish traps are of non-Polynesian origin and that may make them European. But as there was a veritable flood of Europeans through the island from 1937 to 1946 then which Europeans? A puzzle indeed.