Thanks for all the responses.
I should have been more clear in my question - I do realize that the admissions office issues the LL, although my understanding is if the pre-read comes back positive and the coach is willing to provide full support that there are very few instances when a LL (and therefore admission) is not given by the admissions committee (aforementioned timing issues aside). So after the pre-read it really ultimately is up to the coach to select who they support (and hence, while semantically incorrect, it’s the coach’s decision who ultimately gets the LL).