I DON'T THINK THIS IS ACCURATE - it may have been true at one time but these days all of the tours are provided by Delaware North - an independent, for profit tour company.
I have done the "behind the scenes" tour there and it is fantastic - one of the most memorable tours I have ever seen.
You stand on the launching pad for the shuttle rockets. You see the Atlas Rocket that carried men to the moon, and you see many of the lander parts that landed men on the moon. You also walk through the Apollo project control room that took men to the moon (so cool, just like in the movies).
So - my point is that even if you could do as you say, I am not sure what you would see. I highly recommend going to the Kennedy Space Center, but there is no reason to try to get around going on the provided tours with their excellent guides. Plus, the space center is HUGE, you can't "see it" without the transportation managed by Delaware North.