WOOOOW.
That's all it was. It was set to 'Show'. I know I was trying to do this to get the sketch visible, but obviously didn't know what I was doing. I didn't know it was a "show globally" as much as it was "don't make it invisible!".
That completely explains how I was able sometimes to...
I can't figure it out. I've been looking for a while now.
When in 3D view on some of my parts, I see gray sketches of one or more features overlaid. Sure, you can turn it off with View, Sketches, but I want to know what this means.
I used to think it was because they were not fully defined...