I'm sorry, but how do we know that? I think we've just all gotten accustomed to it being possibly wrong on reruns and home video. I would be sure to say that the music changes from year to year, even on an ID like that.
And here is something that makes this a home video phenomenon. On the 2nd season Mission: Impossible DVDs, the 5.1 track has the 1966 recording of the fanfare on episodes from the second half of the season. But if you switch to the 2.0 mono track, the revised recording that I linked to is there. So I'm more inclined to think that the second recording was used on all Desilu/Paramount shows in the 1967-1968 season.