The initial ticket will be issued to Avis. They will search their records and then send in a nomination form ID'ing you as the driver. There isn't really anything you can do about that part, it's company policy.
However, they will not automatically bill your credit card for the ticket. You will simply get the ticket in the mail from the court with your name and picture. I think some car companies do charge you a $30 or so "administrative fee" for ratting you out as the driver.
From that point, you can fight it just like you got it regularly through the mail in your own car. I found some really useful information here:
http://redlightcameradefenders.com/f...ked-questions/
Good luck!