Re: TOS set during the 22nd Century!?
Which doesn't exactly help make it any more plausible.
First you bring up that it makes no sense within the context of other Trek then dismiss when someone brings up a reason it could work within that context. Make up your mind.
I don't think anything in Where No Man...
indicates that the Valiant was where they expected it to be. Kirk's log indicates that it was a missing ship.
"...the most elementary and valuable statement in science, the beginning of wisdom, is I do not know." - Lt. Commander Data, "Where Silence Has Lease"