No, herd immunity does not mean ALL hosts are immune.
It does mean that enough hosts are immune that they protect the remaining non-immune hosts. It is a statistical thing. All of the immune hosts are barricades to the transmission of the virus so some number of non-immune hosts never get infected.
Statistical "immunity" != physical immunity (or, more precisely, protection against infection). A non-immune person may be statistically less-likely to become infected (due to decreased likelihood of exposure) in a herd immunity scenario, but if that non-immune person is exposed to an infected person, that non-immune person is just as likely to become infected as he would be in a non-herd-immunity scenario.
I think that's where we aren't seeing eye-to-eye.