Well, thank you so much for responding Peter. I am happy your response was aligned with my ideas, not because I want to be right above all, but because I was hoping I had understood the main spirit of the rules and the main ideas laid out by the mode's creators. I think it is pretty obvious then that natural objects like boulders, foliage, etc. are not breaking the rule if destroyed, whether it is done by Garrett's hands, weapons, items, and whether there is visible damage or not. Those items do not even fall under the category 'property'. The rule was meant to cover man-made objects. However, there are probably going to be objects that fall somewhere between, and like Peter said "the distinction is arbitrary". Those cases the player will either just have to make a decision and report it, or first come ask here in the discussion thread and based on the consensus of the community hopefully we can come to an agreement. Something we haven't discussed before is if there are readables or story elements that make it obvious that something that appear natural (like icicles) have indeed been constructed by a person (like for example if in Trial of Blood a journal somewhere boasted about a person creating the icicles in order to block the passage for Garrett), then it would fall under the category 'property' because it evidently is someone's construct. But unless the mission says so explicitly, natural objects do not count.
The other thing Peter points out (and marbleman confirmed) is that there has to be visible/audible or implied damage. And it should also take some sort of object/weapon/force in order to damage it. Thus, the wall in Sound of a Burrick is not property damage for two reasons: 1) It is weak enough for Garrett to simply push, and 2) It falls out in one piece, much like a door that can't be closed, and is not fragmented and therefore not damaged. You can imagine two strong guys coming there later and placing the wall piece back, without telling the owner the wall has been destroyed.
This is a difficult distinction to determine. If you have a ruined house with haunts in it, breaking a door to gain access would still be property damage, even though it's not owned by the man who made it any longer, but instead undeads. Or did you mean since it was at one point made by men, then it would be property? Perhaps I misinterpreted. Maybe there won't be that many cases where this becomes applicable even, so perhaps there's no point in making it a rule. If we did, to me spiders, burricks and beasts like that no, people and apebeasts yes, undeads I would also say yes because in some missions there are clever ghosts that talk and make evil contructions. Zombies no, but then again they don't ever make anything (unless it was a modified clever zombie and in that case perhaps could talk). Craymen are sort of borderline. I'd say they probably fall into the beast category. I'm just thinking out loud as I'm writing right now, so let me know what you guys think.