I don't think there is anything "bizarre" about giving a definition of a legal word, explaining how it's used, and then stating exceptions to the rule. Of course a statement is not hearsay unless offered into evidence for the truth of the matter asserted. I am not sure your point there as I never said anything different.
I said quite clearly one can be charged with perjury if they lie under oath and then made clear that hearsay is a statement not made under oath.
Breach of contract in an email? Generally not, there has to be some actual act or threat thereof.