Why do you think Edward can't read Bella's thoughts?
In the series, it's established that it's like Bella's mind is on a different frequency than what Edward is accustomed to. Ms. Meyer has stated that Bella can be influenced by other non-mind related powers such as Alice, who sees the future which is a "non mind" related power in the Twilight world, or Jasper's power to influence which is also "non mind" because it influences the body verses the mind - he uses the pulse and endorphins to influence.
Edward can't see into Bella's mind because her mind is so private and she is such a private person that no one can. I would think it would stand to reason that there are other people out there who are also similarly super private that Edward couldn't read but as most of his life is spent in two very small towns in Alaska and in Washington, he probably just hasn't run across any others.
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