Based on nothing but your message, it appears that you have frequency and harmonic reversed.
A Clark-style device by definition generates harmonics due to the shape of the pulses - square. On an oscilloscope you see what appears to be a single frequency waveform, but it contains an infinite series of component sine waves. The more "square" (sharp-cornered) the wave, the more energy there is out at the harmonic frequencies. She indicates that the effectiveness of her device is dependent on harmonics several ways. Unlike Rife devices and others, the Zapper does not require adjustment to specific frequencies for specific pathogens. Also, her statement about tapping a car battery being effective confirms that it's the harmonics doing the work, because 5-10Hz is awfully low for any direct (non-harmonic) effect on something sensitive to much higher frequencies. The circuit for her shoe-box design is a classic square-wave generator lifted straight off the data sheet for the 555 device. By the way, positive-offset, negative-offset, AC coupled, whatever - the harmonic frequency set is the same.
I'm not quite sure what you mean by "Beck-style" devices, but if you mean such things as frequency generators, then Beck-style devices are based on single frequencies, not harmonics. If the fundamental frequency is not a sine wave, it will contain harmonics, but most of the energy will be in the fundamental tuned for a specific pathogen. To re-word your sentence, a single frequency can kill a parasite
which falls between two of a Zapper's harmonics.
So I think you've got it backwards. Harmonic theory is very much the basis for Clark-style devices, and (broadly speaking) not for Beck-style or Rife-style devices.