For the record, you can toggle off the path highlighting/outline with one of the buttons on the node editing toolbar (you can even change the color of it in preferences).
Thank you! Actually, now I suspect it's a bug... (unless it's one of those "features").
Whether the "Show the outline of the path" is on or off, when you're in edit mode, the red outline flickers on for a second before disappearing again. Since it happens all the time, it's rather distracting, especially when you have "Show the outline of the path" Off so it's basically blinking all the time whenever you're mouse-over or editing the path.
Now I see that it's actually Least annoying when you have "Show the outline of the path" On and have the object selected, because then at least the line is constant.
So? Is this a feature or a bug?