How negotiable is "non-negotiable"

On the initial phone interview with the recruiter they made it very clear that the salary was $120k for less than 12 years experience and $135k for more, and that it was non-negotiable. However, having also interviewed for the Patient Access Manager role, I know for a fact they offer a salary range, between $130-150k.

That being said.. Has anyone actually received an offer yet for the NSS jobs? Is the $120k set 100% in stone, or is there wiggle room?