When people talk about public commits it means commits other people have access too, and more specific, were able to commit on top. Authorization has nothing to do with it. In practice it means anything you have pushed.
An exception can be made for topic branches, especially in a pull-request workflow. These branches could be rebased / amended to update the final result, even after they have been pushed already.
Yeah maybe public isn't a good term for it, I usually use the term stable. So any pushed commits are indeed public, but they are only stable when they reach a stable branch. This means that if I am working on a branch I may remove, add, amend, reorder commits even after I've pushed them. If you constrain rebasing only to unpushed(not public) commits then you instead end up discouraging pushing code to the remote.