The NHTSA are fine with auto-braking - indeed, they want it to be standard on all cars in the future[1]. What they're not OK with is companies marketing glorified cruise control as a self-driving feature. Elon Musk likes to lump his implementation of both under the same "Autopilot" umbrella for PR reasons, but you can have the former without the latter - indeed, I'm pretty sure the most prominent example he gave of the former saving a life was wityh the latter switched off.

[1] http://www.autoblog.com/2016/03/17/nhtsa-iihs-20-automakers-...