You must not be reading my posts, you didn't read up on the central limit theorem (as your complaints are directly addressed by it), and you appear to have no knowledge of statistics. Do you know what it means when the poll says +/- 4% at the 95% confidence level? Do you know what confidence level a 13 point gap corresponds to?
You absolutely don't need to believe that people aren't individuals to believe that polls are accurate, true representations of public opinion. Let me give you some tips for discrediting polls, you're going to want to look at the sample and declare it biased, or you're going to want to attack question ordering, things like that. Attacking the mathematical basis for scientific polling is a bad idea, because it is mathematically proven. ie: it's not open for debate.
You're going to strike out when attacking this poll in those other ways too, but it might be helpful in the future if you see other inconvenient truths that you're trying to ignore.