The latter option means we're short a bench player.
I think the throwing thing Buck mentioned was hearsay because Bautista said after that game something like "there is no update, there is no progress and when there is an update I will let you know." He sounded pissed off, as if he knows he can't throw worth s*** right now. I think the cortisone shot was a last ditch effort to try to avoid a DL stint and realistically that doesn't heal anything it just brings swelling down so there is less pain. It doesn't make anything heal.
If they DL him with the full intention he will not return until he can throw 100%, then he will be gone a lot longer than 15 games. My personal thought is that they felt if they had put him on the DL when the injury happened he would have been sidelined for possibly months, but by playing DH it could actually allow it to heal a bit on its own to the point when they do DL him its only a 15 game stint.
I feel like they are either riding it out as long as possible to make a shorter DL trip or milking out all of his offensive production they can knowing a DL trip would end in surgery or something significant, possibly season ending (torn rotator cuff or something)