Does Apple, inc.have the legal right to information in my notes stored in my iPhone?

I'm concerned about security. This is a spam mail account so I'm untraced.

I store and write 25% of my personal thoughts that I keep free from outside influences in my iPhone device using the current iOS (6 I believe). I'm a private consumer with a contract through AT&T for cellular service. I'm a private US Citizen, and however realised too late that I should have read all terms and conditions in the iOS 6, Apple iPhone and basic AT&T cellular contract.

Is my private data in the Notes app stored on my iPhone device liable to be stolen or observed remotely by Apple, inc or AT &T?

I'm concerned with protecting my freedom of thought from these corporations.

Hopefully someone will answer.

The basic truth that everyone should know about electronic information storing is that if it is done on a device connected to the internet, it is hackable and shareable. Yes, you should have read the contract completely. Your contract probably has some clause that authorizes sharing unless you specifically deny that sharing.
I don't understand why you think you aren't traceable.
Keep numbers and addresses on the phone, not personal info.

Your first mistake is thinking anything on your phone is private and secure.

Your second mistake is assuming anything on a computer connected to the internet is private and secure.

Your third mistake is thinking a throwaway email can't be traced right to your door.

Because obama is already capturing everything americans do today.