>The public phase holds changesets that have been exchanged publicly. Changesets in the public phase are expected to remain in your repository history and are said to be _immutable_
Note that in Git all history is mutable, even if published.
Regarding 'backout' (and 'revert'), to the best of my knowledge, it does not revert commit, it creates a new one (reverting changes), and I frankly do not know is that's possible at all to amend commit in Mercurial (when I worked with it, that was definitely not possilbe, but that was a long time ago)