I have a post-update hook on my server, such that when I
git push
it does a pull on the live web directory. However, while the push always
The hooks are run as the user doing the push. If you have some kind of pre-made setup, that may be a user like git or gitosis, or it may be you. Just look at how you have the remote configured. (git remote show or just examine .git/config if you don't know) Presumably you're pushing via SSH, and there's a username@hostname in the URL.
P.S. It's pretty quick to demonstrate this - just clone a repo locally, throw a post-update hook in with an echo $USER or something similar, and try pushing as yourself or a different user (directly or through ssh).