Yes, that's what I'm saying, but your previous paragraph has peaked my curiosity. You said, "denied it (refused to believe it)". I take it that you think one meaning or sense of "denied" is logically equivalent to "refused to believe it." I have no problem with you refusing to believe something so long as there's something to refuse to believe, so if you can show that they can rightfully be considered synonymous, then I suppose you got me.
Well, I'd post an entry from an online dictionary (as I've previously done), or something supporting the claim that in formal logic one may use "deny" to mean "negation" (again, another example where one need not claim anything), but I think you know about both of these.
But, notice the example. There are implications.
is where the basis of your argument lies, isn't it? What do you mean by, "There are implications"?