I did not say that they are identical, so I did not say that Shakespeare is the author of Hamlet . If what I said of one man is true of him iff what I said of the other is true of him, the issue is obscured. So suppose the belief is false. Then the second thought would be true. No time factor is involved.
People can make all sorts of mistakes about what is going on in their minds.
The argument holds for any mental state that has specific content. Sensations are, following tradition, said to be objects of sensory experiences. Armstrong has argued that reports about sensation can be mistaken without verbal confusion. This is the example of brain state 143. The story is that neurological science correlates it with a sensation of red, but the person under the scope and under the influence of truth serum reports having a sensation of red, without being in state 143.