That is an interesting experiment you highlighted. I was not aware of it. I will point out though that the group that did not want to seem out of step were seemed to be the lest numerous. So while agreeableness seems to have a certain correlation to independent thought I do no think that for the majority of people that is the main blocking point.
I think I know myself pretty well, better than most, and this allows me to make a pretty good guess about the way I would react. I think that if I were to answer wrongly to the Ash experiments, I would do so because of what is described in the Wikipedia entry as "distortion of judgment". This stems mostly from my view of the world and my belief that human observation, without aiding tools and methods of quantification, can be very unreliable. That applies for me as well, leading to poor confidence in my direct observation.
Thankfully, creating new ideas or solutions has several steps, observation being just one of them, another being the processing of the stimuli into the final idea. This, I consider, is where I am far better than the observation stage. Given a set of observations I arrive at a pretty complex solution and/or idea, and this is where most of my deviation from the norm usually stems. But I am aware of the possibility of mistaken input data of vicing this process, and forming the wrong conclusion because of it.
Anyways, sorry if I came of a bit arrogant, this was more of an introspection exercise and me musing and a little bit over-generalizing about the way people think.