There's obviously something more to it than simply having a very strong advanced haki, starting by the obvious detail that, if you can destroy Kaido from inside, then you don't need to cut him to begin with. Hyogoro never stated that connecting with your sword is a power that requires the level of armament that allows you to hurt something from the inside, may I ask why should I believe that Mihawk or Ryuma have ever achieved such level of armament only because their sword is black, which will more than likely be related to becoming one with your sword? (which isn't loving your sword a lot because you've had it since childhood but being able to transfer your will in congruence to every material's breath).
"Oden was able to cut Kaido", so? Is cutting Kaido the pinacle of swordsmanship? Does it equal to being able to cut anything but nothing at the same time? Was Oden a master of this power because of it?
And I'm not arguing that BOAT isn't haki but pointing out that it is a retconning that needs way more explanation to make any sense.