On OSRS the items are shared AFAIK, so getting a drop once completes it for all. At first I thought it was really weird to mark drops for NPC's you didn't get them from, but it's just another way of looking at it I guess. Then the collection log is more a way of asking: is there anything I can get from this NPC that I don't have yet?
We can go either way on this. It's whatever you guys prefer.
PS: Anyone who suggests togglescape will have to get each drop 10 times to get it marked.

EDIT: One very important thing to note:
The vast majority of these shared items are not actually NPC drops. They are shared between chests, easy/hard/elite treasure trails, mystery boxes etc. So although it would no longer give you an accurate representation of how many you got from each, it might be better to share them anyway because it'd be a royal pain to have to obtain all the items from all those possible sources.