Ability to set Requester:Organization from Triggers

When a customer emails in for the first time, it would be really useful to have a Trigger set the "Requester:Organization"...With multiple email addresses configured in ZD, this gives me the ability to automatically associate an end-user to an Organization based on where they sent their email to.

I can create a custom field and have that set, but I can't set the Requester's Organization....making the built-in Organization field useless to me.