From 19 years of personal experience as a captain on the A320, I can confidently state that 90%+ of the pilots I fly with don't put any crosswind correction in for the takeoff roll. On rotation with a strong crosswind, there is usually a rudder wag and quick correction as the nose comes up and the plane tries to simultaneoulsy roll away from the wind and weathervane into the wind. This fits what we know so far.
My inital instructor at Airbus told us to not use crosswind aileron inputs because the computers would take care of it and you didn't want to get spoiler extension. This was proved patently incorrect and it's now clearly spelled out in the FCOM. I had a new FO right out of IOE that could not land the plane. Upon discussing his difficulties, he said he was taught (at Airbus Miami) to never use cross-controls for landing. With some new knowlege and coaching, he was easily able to handle crosswinds. Again, I suspect there is some old, bad tribal knowledge still out there.
I'd place a bet on this being a factor.