Since the passive piezo is bipolar, only integrated oscillators are polar with Red black.
If 1mV modulation is applied to a high voltage modulated carrier, be it internal oscillator powered by 12V or ring voltage at 200V would have a modulation index such microscopic proportions not only from impedance ratios but modulation index, it would have no practical RF emanation levels even if direct connected to a sophisticated spectrum Analyzer.
This is why RFID's dont use VLF.