I think the point was that the universe into which Kirk and the Defiant vanished was an empty one- a 'null space' with no matter, light, or anything else. That would mean it couldn't be the Enterprise mirror-verse.
However, since there are infinite quantum universes (as shown in TNG's 'Parallels'), it's possible that a near-inifinite number of USS Defiants went through interphase and emerged in a near infinite number of parallel universes. Which would explain why in TOS the Defiant crewmembers wore the same patch as the Enterprise crewmembers, but the Enterprise mirror-verse Defiant's crewmembers wore a different patch.
Of course, ALL of this is nothing but a way of explaining away production and/or continuity errors in various works of fiction.