Advanced Alerts were designed to be "push" alerts in which a single author creates a VizAlert that is used to email multiple users based on the Email To field. It is not designed to be an opt-in scenario, which is why only the author can subscribe to an advanced alert to set it up.
This is behavior that we do intend to change, however: Allow non-owners to drive VizAlert execution · Issue #119 · tableau/VizAlerts · GitHub
This is where it's being checked in the code: VizAlerts/vizalert.py at master · tableau/VizAlerts · GitHub (though I can't say that editing this is a good idea, without testing and considering any other places that assume the subscriber is the owner).
What is custom about the emails that you want to be sent out? If it's simply sending an image of the viz, using some custom criteria based on the filter selections, you may not need VizAlerts at all for it, but could use a conditional subscription or data-driven alert.