It most certainly DOES include SwO damage. I just tested this to confirm it, as I thought you might be on to something. But nope, ACT again is very accurate at what it does, especially on the client running it. Anyway, I did 3 runs with SwO on where I only auto-attack for 2:30 and then 3 runs with no stance where I again only auto-attack for 2:30. I just uploaded the results to the same Dropbox folder.
It's listed as a skill/ability, as shown HERE.
On another note my video upload had an error and didn't complete. Don't fret, I'll try again tonight.