The fob is not transmitting 24X7
No doubt. But that's because it has a button to press to transmit. The keyless ignition fobs have no button. While they also don't transmit 24x7 I think they can be interrogated at any time.
The fob is not transmitting 24X7
There’s the kind you are referring to, which only does something when you push the button.
There’s also the kind which let anyone with a fob just walk up, pull the handle to open the door, and push a button to start the car - while merely carrying the fob. It is most likely only this latter kind which is being spoken of.