Well u never know with Kenjaku ( i just don't see why he had to "lie" when we found out Sukuna's old Body, in that particular situation Tengen was no longer a threat )
And let's not forget that at some point he even said it wouldn't matter if Sukuna would reincarnate or not ? Just his presence alone would be enough so that's indeed sketchy....
My guess for now is that this is how events happened to have happened...
Kenjaku needed Sukuna for something not necessarily reincarnated, just his presence, which would have probably been less troublesome for him to handle lol ( especially since Gojo was out of the picture at that time ).
However he let Urahume complete the bath thing " just in case "
Now the fact that he could only use Sukuna's presence inside someone as a vessel and not necessarily him reincarnated makes me think how these binding vows really work.......
When Sukuna made a binding vow with Yuji he said that if he was to break it HE ( his soul ) would be the one to be punished not Yuji
So maybe what will Kenjaku do will extinguish Sukuna's Soul ( after he took down all the threats ) leaving him and Megumi alive
Or he just made that rule after Sukuna took over Megumi so it could just be that he had to add it after Sukuna completed the bath and it happened to be in Megumi's body and the " rule " works differently than a binding vow so Body & Soul could be the same thing like Him, Megumi ( and whatever soul it's inside him ) need to be alive at the end