Hard to say who really started it without the rear view. My guess is that the biker had been gaining fast on the car and once behind began to push through, splitting lanes, and the driver was uncomfortable with how close he was and moved over. Just speculating.
In the end, the law and insurance will place the blame on the last driver.
You're always going to be passing on the right of one lane if you're splitting - left of one, right of another - otherwise you're passing on the shoulder. Or is that considered splitting as well? Serious question, I have no idea, just assumed using the shoulder is always illegal except in an emergency so not an option for splitting.
You hit it on the head anyway with "between two lanes of slow moving traffic". Traffic in the HOV lane was moving quickly outright plus considerably faster than the lane to the right; not legal splitting given the circumstances...assuming I understand the rules.
"Straight roads are for fast cars, turns are for fast drivers." ~Colin McRae