You don't have to delete your local branch.
Simply delete your remote tracking branch:
git branch -d -r origin/<remote branch name>
(This will not delete the branch on the remote repo!)
See "Having a hard time understanding git-fetch"
there's no such concept of local tracking branches, only remote tracking branches. So origin/master is a remote tracking branch for master in the origin repo
As mentioned in Dobes Vandermeer's answer, you also need to reset the configuration associated to the local branch:
git config --unset branch.<branch>.remote
git config --unset branch.<branch>.merge
That will make any push/pull completely unaware of origin/.
Source: http://stackoverflow.com/questions/3046436/how-do-you-stop-tracking-a-remote-branch-in-git
I'd agree that the terminology can be real tricky some times, especially when its the devs that write the docs, so assume everyone is not that far behind them in their understanding (one of the Kruger-Dunning effect corollaries).
The 'rtb' is a bit 'reverse polish' in that it's actually "the branch that tracks the remote (repository", but never really explained anywhere (in the sense you mentioned about the potential confusion) The glossary rtb is what we get.
Even this (rtb definition) subtly isn't quite right because of the confusion about what "latest" means, who does it and when (i.e. the rtb may be out of date, but the fetch and pull commands are the ones to actually do the update - the user needs to do the command, it's not automatic!)