This would be true if your offer was negotiated with a distant bureaucratic committee (or board), but most of the time, regardless of who they represent, you're just dealing with people.
Actually, that sounds like a great reason to volunteer my current salary. As long as I'm not desperate I don't want to work for a company that maintains such an idiotic policy, because it tells me something about how they view and value their employees.
If HR is that bad, and the organization gives HR that kind of power, how can you say the organization is "quite good"?