I think I know how this device works.
The remotes use a Rolling Code that changes based on a random number generator (not really random but based on a seed number and a formula). Every time you hit one of the buttons on your remote, it sends a signal to the receiver in the vehicle and and the remote generates the next random number as does the Receiver so it knows what the next code will be when that remote is used again.
If you hit one of the buttons on your remote while you are out of range of your vehicle, the remote increments to the next random number, but the receiver does not know that the code was changed. So to prevent problems, the manufacturers allows the receiver to check the next 256 random codes in sequence, that synchronizes the receiver and remote. It does this so fast that you never realize that it was ever out of sync.
I think this device must know how the random number generator works, and and can predict the next 256 codes. Simply repeatedly pressing the button on the mystery box will generate the next 256 codes and the next 256 codes in sequence. That can amount to trying thousands of codes in just a few button presses. The rest may be just luck that they hit the right code quickly, or they just move on to the next vehicle???
...Rich