I really wish vBulletin would have a master switch in the Admin CP to disable this often unwanted function.
Here is what you have to do to make sure users don't add edited by information when editing a post.
Open the editpost template and comment out the following code.
Code:
<!-- do not show next section edited by -->
<!--
<div class="smallfont" style="margin-bottom:$stylevar[formspacer]px">
<div>$vbphrase[reason_for_editing]:</div>
<div><input type="text" class="bginput" name="reason" value="$newpost[reason]" size="50" maxlength="200" tabindex="1" title="$vbphrase[optional]" /></div>
</div>
-->