I don't agree (obviously
). There is no reason to show us that purse on Enterprise unless to strongly indicate that T'Pol's "story" was in fact true. If fact, T'Pol's service record did provide positive proof she went to Carbon Creek.
Of course, we do get a clue that the story can't be exactly
as T'Pol told it: T'Mir gets invited to a minor-league baseball game during a time when Sputnik 1 can be seen, and that that places the action between October 1957 and January 1958.
Mind, this is well within the normal bounds for mistaken recollections or errors in transmitting stories, and the moreso considering it'd be across several centuries and possibly multiple generations of storytelling, and so can only really be used to foil Bugs Meany.