[rewboss]

Consider:

Bill said it may rain yesterday.

That sounds rather unnatural. Nobody would say that -- I've certainly never heard or read anything like that.

The possibility that things may be different yesterday than they actually were is exactly zero. How would you go about, for example, making a cake yesterday? It can't be done. In fact, some scientists believe it would be impossible even if you had a time travel machine. But the day before yesterday, the possibility of making that cake was still pretty strong.

Bill said it might rain yesterday -- but he was wrong.