First of all lets clear up terminology.
webmail is a mail client web-based application like Squirrelmail, Roundcube or Gmail.
formmail is the term for messages sent from forms filled out on a web page, such as the contact page in question.
Yeah I don't think he meant webmail as in a CGI IMAP/SMTP client like Squirrelmail or Roundcube though. He is mentioning the messages are sent from the DreamHost-provided formmail and accessed directly by Outlook.
From: System <firstname.lastname@example.org>
So this is what the tech was referring to. I hope this much is clear.
Also earlier I had mentioned another issue that the formmail message might be in "TEXT" format and might need to be sent in "HTML" format instead. Since she uses a logo, I'm assuming her normal messages are sent out in "HTML" format.
Now Outlook is apparently checking how the message headers are filled out and whether the message arrived in "HTML" or "TEXT" format. Then it determines how to compose a reply message.
So I would suggest asking her for a copy of a message (get the "raw" version including message headers) of a message that works as expected when she goes to reply. And then develop a separate formmail script to mirror the format.
However that might not work, it could also be that Outlook is using information in her address book and determining how to compose a message based on who she is replying to.
Edit: I don't use Outlook myself. But Googling for configuration tutorials I found out that you can use a different signature for replies and forwards then one used for new messages. One might want to review http://office.microsoft.com/training/Training.aspx?AssetID=RC101861341033&CTT=6&Origin=RC101861341033 if you need someone to lecture you more on the subject =)