I will say it's a misinformation as assistants don't actively record the surroundings to detect "Wake Words". This is typically done by the device itself in a passive state using low-power components like Digital Signal Processor (DSP) without actually recording or processing any audio signal.
That may be for another sort of AI assistant but an example is google Assistant that does not use this system and in fact even offers playback of what's recorded through the google home app. If you could link a source that I can look through that'd be awesome I do appreciate your input. :)