Speculation. The GM is in charge of the coaching to do with what he wants. The comments in the presser are standard lip service. You're not going to dump all over a guy you want to want to have be part of the process. As I've said in the past too, if you want him out from behind the bench, promote him up.
There's three ways to go about this:
1. Sullivan is fired and removed from the organization (which I would be fine with)
2. Sullivan is removed from being head coach but is kept in the organization (which I would be fine with)
3. Sullivan is retained as head coach (which I would not be fine with).
As @mmp9 said though, could be a standard mid-season firing if they continue to struggle.
That said, I do believe that Sid and possibly Geno/Letang may have a say in this as well. If there is anyone on the fence, that could sway the decision either way. I would go so far as to suggest that they were much more mushy and gushy on Sid than Sullivan. They said "it's very important Sid never plays in another jersey". They said "we think Sullivan is a rock star" not "It's very important to us that Sullivan coach no where else"
I guess I'm just taking the lip service more with a grain of salt than others because that is literally what FSG should be doing.