they did not understand what "the Big Bang" meant in the context of the survey, and neither did they understand what "Natural Selection" meant
They didn't understand what concept was being referred to with the term? If instead the questioner had described the big bang (without using the term "big bang") would the respondents have given a different answer? Possibly.
I think for many people the "don't accept" comes less from a actual rejection of the theory, and more from a position that the theory is irrelevant and ultimately unimportant.
You have to admit, the big bang theory is really pretty esoteric.
There is also the on-going problem with the big bang theory in some peoples minds that there is no consensus at to where the matter and energy that composed it originally came from.