I've worked for 2 large technology companies. The first was a big one down in Southern California and HR there was as you describe.
The other was a big one in San Francisco, and their HR was insanely powerful... for some reason. It was quite a shock to me but to a lot of others used to Bay Area startups they made it seem like the norm.
So I guess my point is that not all HR is alike and there is probably some truth to this HR negotiating business.
But they are the ones having the actual conversation and working the rhetoric to close a deal. They aren't Deciders, but they are Negotiators ("salespeople").