It’s good that you’re concerned about the data your phone may be revealing to other nearby devices. It’s generally a good idea to have bluetooth/wifi/nfc turned off if you’re not actively using them. Even without the robot, you have no idea what data companies might be collecting when you’re physically on their property.
https://security.stackexchange.com/questions/62124/phones-broadcast-the-ssids-of-all-networks-they-have-ever-connected-to-how-can
I think the lady said they know the IP address of every phone but that doesnt make much sense. anyway, the point was that theyre using the signals from your phone to uniquely identify you. you can simply turn those radios in your phone off when youre not using them.