We sometimes say that someone said something other than they meant to. And we're quite serious about claiming that they said that thing that they misspoke. "He meant to say 'I need a new watertank' but said that he needs a new riverbank."
But suppose I mean to say: "I don't like the hair", but I misspeak and omit the "h". What did I say? Was it that I don't like the air or that I don't like the heir?
It might here depend exactly at which level the mistake is made. If it is a mere mispronunciation, we cannot say whether it was air or heir that I said I didn't like. In fact, I think in that case I didn't say either. In cases of mere mispronunciation it seems accurate to say that I said I don't like the hair but I pronounced it wrong.
But the error could have happened at the level of word choice: I might have chosen "air" in place of "hair", accidentally. I might even have seen a flash of the written representation before my mind's eye (that sometimes happens to me when I hear or say homonyms: I am one of those people for whom the written language is primary). In such cases, in principle, analyzing my brain could reveal that I in fact used "air". This is not a case of mispronunciation but use of the wrong word. Maybe.
But can a principled distinction be drawn between the case of mispronunciation and the case of using the wrong word? I have my doubts. So perhaps we should put very little weight on the "but said..." in cases of misspeaking, and not even take literally my opening example of "said that that he needs a new riverbank." We can correctly say that he uttered the sounds "I need a new riverbank", but I am not sure we can say that he actually said that he needed a new riverbank. (Almost surely he didn't assert it.)
Maybe where we want to draw the distinctions is in the success of communication. If the listener can correctly tell what the speaker meant to say, then we can say: "He successfully communicated that...". If the listener misunderstands, then we can say: "He tried to communicate that..., but instead what he got across is that..." (note that the listener's misunderstanding may or may not be the speaker's fault in general, so we may want to add: "due to misspeaking" or "due to the listener's mishearing"; or the flaw could be joint; or it could just be due to background noise.) And the final case is where the listener just doesn't get it, and then we simply say that the speaker failed to communicate his message (again, there is the question of who, if anyone, screwed up). This shifts attention away from the one-sided stuff--"What is said"--to the joint activity of communication.