Nothing in the surrounding language suggests the belief concerns the general ability to study how people think. Rather, the belief involves how we make inferences about our own thoughts; it doesn’t involve how we study our ability to make inferences.

There’s no suggestion that the claim has often been misunderstood. Rather, the author suggests that psychologists do understand the claim, but their argument do not require them to make that claim.

There’s no evidence that this claim describes a view that anyone ever accepted. The prevailing view described in the passage is that we know our own thoughts directly.

The author does not believe the claim is sound. That’s why the author says it would be “perilous” to make that claim — because it’s not sound.

Supported. The author identifies the belief as something that the psychologists come “perilously close” to claiming. “Perilous” means risky or dangerous. Why would it be risky or dangerous to make this claim? Because there must be something about it that would harm the psychologists’ argument. The psychologists are dangerously close to making a claim that isn’t convincing or would otherwise cast doubt on their overall position. So the author’s belief about this claim is that it’s something implausible or unlikely to be true. (E) comes closest to capturing this opinion about the claim.