I don't think there are many houses period in that area, although it's been a year or so since I've been out there and I may not be remembering correctly.
It's kind of a weird area, in that it's well-traveled and close to Portland but is also pretty rugged and definitely has potential to be dangerous. I think that due to the popularity of the area a lot of people don't adequately respect the possibility of things going wrong (and I would for sure include myself in this group haha), although in Annie's case, being from out of town, she might have had less of a preconception of the area than someone who grew up there.
I obviously don't know exactly where she was hiking in terms of public vs private, but it seems overwhelmingly likely that she was on or near public trails. There are a ton of them in that part of the gorge. The specific one mentioned that they thought was her destination is not one that I'm personally familiar with.