Agreed, but that doesn't mean, in any way, that he could have had his Mangekyou Sharingan the whole time since either Obito or Rin died. Obito died ~20ish years ago and Rin also died some time ago. If he had it all along then he would have mastered his Mangekyou Sharingan and Kamui YEARS ago.
Considering the fact that Kakashi couldn't control Kamui when he first used it on Deidara and now he's completely mastered it to being able to warp away Susano's arrows, hardly a year has pasted. If he had his Mangekyou Sharingan all that time since Obito or Rin died, then he would have mastered Kamui before the series began and would have used it.
It's more reasonable that he developed it over the time skip.