I can believe it. My nephews are identical twins, and not at all identical. They look very similar, of course, and are nearly indistinguishable if they style their hair exactly the same and wear the same clothes, but they have very different personalities. One of them is even gay, but the other is straight. One is outgoing, the other is a quiet introvert, etc.

Colloquially the family has always called them mirror image twins, because coincidentally they had some early moles on their face that happened to be on opposite sides from each other, but IIRC the term actually means something else. They are in fact monozygotic.