No, I don't think it's currently possibly [from the entry section]. You'll always end up with a new file, filename and URL, if an asset already exists with the same file name. To be able to upload an updated version of that asset, you'd need to properly delete the old file first.
There was a related feature request on +g not long ago. Jamie Wade asked to make it possible to delete (and rename) assets through the asset field while editing an entry. If this get's implemented, your client should be able to update the assets with ease. You should just tell him the difference between the minus sign (to just remove the relation), and the UI for proper deletion.
This is only true, if you're dealing with assets from the entry section the the Control Panel. Currently the best way to replace / update assets is through the assets section in the CP (see Peter's answer), some things probably change with Craft 2.2 though.