Wow, this thread is unnerving.
I think that a big part of the problem might be the combination of people that change lanes without signalling (a shockingly large number of people either don't signal at all, or only signal the 3-blink tap to say "by the way, you already noticed me crossing the line, but I'm coming through, beep beep"). Personally, it's a deeply engrained habit for me to treat lane lines like railroad tracks or walls, and only cross them when my blinker is on to indicate what I'm doing or intend to be doing. That's the only time you should be crossing lines... and that's what I do.
About once a week, I find the car completely freaking-out for what seems to be no good reason, but I find it happening most frequently at driveways coming off a striped road - both left and right turns seem to do it. I use AP a lot, and it seems like maybe it corresponds with its sensing of "Autopilot was disengaged, now the car is drifting out of lane" sort-of logic. It really SHOULD be inhibiting all of those warnings if I have a blinker on, for what should be obvious reasons. It seems that even though my blinker is on, the car is like "WOA I DONT KNOW WHAT IS HAPPENING, AIEEE FREAKOUT".
It never applies any corrective steering, though, except maybe once or twice in my now 65,000 miles (probably 20k of which with HW3, now).
I "scheduled service" to try to bring this to someone's attention at Tesla today, after doing a "bug report" immediately after it happened. Maybe that'll help them track this down. It's really jarring when it happens and I'd think that simply inhibiting it when your blinker is on would go a long way to preventing it.
