Can't they just limit the activation frequency? Seems easy enough
The audio system has an A/D converter which samples audio at a specific rate -- say 48 KHz. Aliasing occurs when the input to the D/A convert is above 1/2 the sample rate. A 24001 Hz signal is indistinguishable from a 23999 Hz signal. A 25000 Hz signal is indistinguishible from a 23000 Hz signal, etc.
To eliminate these types of problems, there will be an analog lowpass filter before the sampling circuit. There is a gradual rolloff of signal sensitivity. Aliasing still occurs, but the energy of the aliased signals is significantly reduced.
My guess is you take a voice command, even if it constrained to be say 200 Hz to 2KHz, then invert the spectrum and shift it to the 46-48 KHz range. When this high frequency is played back, due to aliasing, the software after the A/D converter sees it as a 0-2KHz signal, though greatly attenuated. To overcome that, the source audio can be tremendously loud. Humans can't hear it, so it remains stealthy.
Based on flipping through the pages of the paper (https://arxiv.org/pdf/1708.09537.pdf), it looks like they're taking advantage of the non-linearity in the response at high frequencies to effectively demodulate a lower-frequency signal that was mixed up to ~22 KHz.
Which, if that's what they're doing, is totally awesome!