OK, maybe there's a point I'm missing here, but it SEEMS to me that the only difference between 'fighting with an orc' and 'searching for something someone hid' is that the other character 'the orc' is present in the moment. There's STILL a contest going on here. Even if the situation is 'man against environment', you can traditionally see that as a sort of conflict (climbing a wall might be an example). True PvP, I haven't really analyzed that, but I assume you were including NPCs in your comments.
I would say that all the same factors really apply here. I mean, suppose I personally am not super convincing, but my character role in the Braunstein is 'ambassador to East Bissel' or something. ALL of the same considerations that apply in our discussions of D&D apply here. I am not sure that the existence or lack of a 'party' is all that determinative. So, overall, I'm not sure we disagree much, but then you did say "not quite",

. So maybe we almost totally agree.