Apparently someone came up with code to put in a custom module that will remedy this issue:
I've yet to try it though.
I tried out an altered version and it worked for me. Here's what I had:
name = E-mail Sender Override
description = Overrides the 'Sender' of an e-mail message with the 'From' address.
core = 7.x
package = Webform
* Mail altering function to override the 'Sender' of a mail message with the address
* in the 'From' field.
* Alters the sender of the e-mail message to be the same as the 'From' address.
* Taken from: http://drupal.org/node/461324
* See also: http://api.drupal.org/api/drupal/includes!mail.inc/function/drupal_mail/6#comment-3243
* @param message
* the full e-mail message being sent -- this will be altered
$message['headers']['Sender'] = $message['headers']['From'];