Yes, I am aware there are some contradictions, which is part of the problem. The std manual is for the std filter, and the supplement will cover the unique CVO items, including the heavy breather.
If you look at the filter closely, behind the wire mesh, if you see a white cotton gauze material, that must be oiled. The paper is distinctly different - and I don't believe I've seen a heavy breather with a paper version. Just double-check it to be safe.
On the rain sock, we tend to get a lot of those floaty cottonwood seed things, which can quickly get embedded in the filter and clog it up. Worse, it's almost impossible to remove them without destroying the filter, so I leave mine on all the time.
That said, I do suspect that although K&N claims it doesn't effect the flow, I'm sure it might a tiny bit. Certainly not enough to cause a problem for normal use. However, if I was to go to the track, or be in the midst of a Pinks episode, I'd probably ditch it - until the commercial.