As I noted in my post, though, marks don't have to be registered in order to be protected. Even if BCBS doesn't have any instances of the blue cross alone registered with the USPTO[0], that doesn't mean that BCBS couldn't still have trademark rights to it.
> while we have a reasonable likelihood of prevailing our use of the mark
I'm not convinced - there are many (seemingly) clearer-cut cases that have gone the other way. I'm not saying that this is the ideal state of trademark law, but I think that there's reasonable precedent for it.
> they have enough money to try to enforce the mark without putting a dent in their litigation budget
I agree that this is probably the dominant reason.
[0] Which I would not necessarily conclude based solely on the fact that you couldn't find it. It's not a comment on your searching skills; I've used it before, and TESS (the USPTO database search) sucks.