Well, the media isn't "making things up", in this case... The statistic comes from a Quinnipiac Poll, here
The trouble, I think, is the same as with so many other things. Issues are not defined and the respondents are not necessarily educated on the topic. So, the opinions are uniformed.
My own father often has "opinions" that are directly contrary to his core beliefs. He hears things that his co-workers are parroting from this or that news outlet, flavored with their own interpretation/agenda and he assumes it's true.
After I explain the "other side", his opinions come back inline with his general world-view.
Still happily answering to the call-sign Peetza.
The problem, as you so eloquently put it, is choice.
He is no fool who gives what he can not keep to gain what he can not lose.
-Jim Eliott, paraphrasing Philip Henry.