This is also incorrect as most portable fridges have a low-voltage cut off to auto shut-off if the voltage of the 12v power source gets too low. Some fridges even let you set a variable H/M/Low voltage cut-off so you aren’t left with just one option.Connecting directly to the Y's onboard battery will kill it in a few hours if the car is not running so not a good alternative.
That being said I usually use an external battery for when the car is off but it’s not exactly correct to indicate leaving a fridge connected to a vehicle could deplete the onboard 12v battery.