The poll is a little bit loaded. I voted the second one before I realized that you say in the others "can produce". Also, it's not up to the school to produce intelligent students; it's up to them to produce educated students. Teaching someone math, reading and history isn't going to increase their intelligence, only their amount of knowledge.
Of course any school can produce smart students. I don't know the numbers, but I'd be willing to bet that a larger percentage of private-school students come out with more knowledge than public-school students. On average, public school students aren't any dumber than private school students. The difference is the environment. Private schools can have bad environments just like public schools, but I'm pretty sure a higher percentage of private schools have an environment conducive to learning.
If the question is "Are all public-school kids stupid?" , then the answer is, of course, no. If the question is simply "Can public schools produce intelligent, informed kids?", then the answer is yes. If the question is "Do public schools do a worse job of educating our kids?", then the answer, I believe, is yes.