Nope, parent is correct. If you use hg's changeset evolution and run rebase, and then do a hg log --graph --hidden you can see that your original commits have not been touched, other than to mark them as hidden and obsolete.
They both work the same here, I just used hg because it illustrates the inner workings nicely. With git you don't get the nice hidden commits view, just the refleg (which is trying to show you the same thing).