I "thought" the way the Ezpass system (NYC metro area works) is if it reads an EzPass transponder it charges that one (your personal). If not, it uses the license plate of the car to determine what to charge/how much to charge based on if plates are linked to an EzPass account already. Has this changed recently?
I routinely rent when returning from LGA or JFK and drive the car home but purposely been using the 59th Street bridge to avoid any tolls on the ways back. The method above used to work for me 4-5 years ago. Interested to see if things have changed.