I know
this was covered five years ago, but I just got a "check" and have been researching the scam.
Budget Rent A Car Gives Out Your Credit Card Number To Scammers
More On Negative Option Billing and Preaquired Account Marketing
So even though Budget Rental and Trilegiant are now separate supposedly companies, any time your rent with Budget they can give your credit card information to scammers.
According to the solicitation, the "membership" will be charged to the "credit card on file with Budget" and they "are not affiliated with Budget".
I am researching how they get around their credit card merchant agreement to perpetrate this.