Well, only if the transmission is signed & trusted. Otherwise, an attacker could just spoof a payment by transmitting a modified blockchain close to the payment terminal.
Also, things like DVB tuners are not exactly cheap enough to be integrated into many devices (though FM receivers, which may be used in the future, are).
Also, things like DVB tuners are not exactly cheap enough to be integrated into many devices (though FM receivers, which may be used in the future, are).