Common sense says you have to recover the carcass first to confirm that you have in fact killed an animal, but once you do, then you must tag it immediately - that pretty much etches it in stone. I shot a goat back home years ago; it fell off a ledge. It took some 3-hours to safely reach the carcass. When we got to the carcass, I confirmed that the goat was dead, notched my tag, slipped the tag in a durable plastic pouch I carried specifically for that purpose, & secured it inside of the goat's ear thus ensuring I wouldn't deface or lose it on the pack-out. A warden observed the entire hunt from stalk to recovery; he even helped me get it to a spot where I could gut it safely. I received no ticket. "Immediately upon killing" is a pretty simple concept; you obviously have to confirm that the animal is dead/"killed." The reg doesn't say "notch tag upon firing a shot." Nor would establishing a time limit to find a downed or wounded critter be feasible. Folks are making this much more complex than it is. The Op in question recovered the elk but did NOT notch & attach his tag immediately upon recovery. I didn't author that regulation, but I religiously & successfully complied with it over many years on many successful big game hunts with no issues. After a recovered carcass was immediately tagged, then came time for high-fives, hero shots, gutting/skinning, etc. Recognize why tagging regulations in their various prescribed forms exist -- to thwart those out there who would attempt to harvest more than their fair share of game animals by reusing a tag. No, I'm NOT saying that was the intent in the Op's case, but it is why such regulations exist. No one other than the "elder statesmen" knows what their intent was, but I'll take the Op's story at face value; we also have to acknowledge the fact that he failed to notch & affix his tag to the carcass immediately upon recovery. Regulations aren't perfect, but inconsistently-applied regulations are even less-perfect and do generate confusion. As I said earlier, I'm sorry for the hunter's grief, but he made the mistake not the warden who was just doing his job.
Folks have debated my factual rationale, but not one of you has answered this question, which is at the heart of the matter: "Can you give me a valid reason why willful non-compliance with any law/regulation even "just a little bit" should be okay (excluding life or death scenarios)?" Hunters both local & non-resident have not had an issue with this particular regulatory requirement for many years, excluding those who failed to comply & were caught doing so. I guess my final thought on the topic is this: If you aren't willing to understand & comply with hunting regulations and don't want to risk a citation, don't hunt.