It does indeed depend on the circumstances. In a desert, things take approximately forever to decompose; they just desiccate. In a wet environment like the Eastern forests, organic refuse is less of a problem - but it still draws nuisance wildlife to the areas humans frequent, so pack it out anyway. You packed it in! You haven’t had a segmentation fault, so don’t dump your core.
Organic refuse from native materials is pretty fair game. If you happen (lawfully, I hope!) to catch and eat a fish, harvest fruit or nuts, and so on, during your travels, depositing the inedible portions in the places where they’d ordinarily wind up is acceptable practice. (It seems strange to a conservationist at first, but returning fish offal to the waterbody where you caught the fish is supporting part of the fish’s food web. Sooner or later, that dead fish was going to be in that water whether you caught it or not.)
WAG bags, poop tubes, and the like are needed above treeline or in some extremely arid conditions, but are overkill for well-watered woodland, where stuff decomposes fast and proper compliance with Deuteronomy 23:13 suffices. If you can’t comply because of frozen ground in the winter, then spread that which comes from you as thin as possible so that solar UV will disinfect it, and wipe with a snowball so that there’s no TP to manage. A snowball isn’t nearly as unpleasant as it sounds.
I have had the experience of returning to a campsite about a year after I previously stayed there, and out of curiosity reusing the site of a previous cathole. It was pretty much indistinguishable from when I dug it the first time - no sign of TP or that which the TP cleaned up after.
Obviously, any instructions from the land manager should take precedence over mine.
(and now I’m remembering an argument I had with a state employee at a campground recycling center - “You’re supposed to leave the labels on the cans!” “Uhm, this isn’t my trash. I was hiking in the backcountry for the last three days, and this is garbage that I cleaned out of campsites.” “But you’re supposed to leave the labels on the cans.” “There were no labels on the cans when I picked them up. I was cleaning up after someone else.” “But your’re supposed to leave the labels on the cans!” et cetera,)