What kind of diffs? Diffs between committed versions will typically both have $Id$. For diffs between checked out files and the repository, git replaces the $Id: ... $ string with $Id$ before the comparison.
Hmm... It does however seem like the git documentation isn't correct; it seems also $Id: ... $ strings are replaced on checkout.
FYI: I've now patched the git source code to fix several issues (the above among others) with git's handling of the `ident` attribute. The courageous can try the patches on the grubba/ident branch of git://pike-git.lysator.liu.se/git.git/.git