It’s not really hidden. In the interface you can play back your previous messages. It only stores stuff you say when you say ‘alexa….’ though. It’s not always listening because people have looked at the packets coming out of it and they truly only send a signal when you want them to.
These messages are not stored on the device itself. Oh, no, they are stored on the Cloud and just played back through the device. The dumber the device the better. Device processing power is used for Digital/Analog Conversion and Communications. Good Digital/Analog Conversion is not cheap.
I’d be willing to bet money that the Cloud does all the voice recognition except the ‘Alexia’ part. The device just buffers the message, passes it up to the Cloud where the real horsepower resides. How else could they get someone else’s messages? That’s how I’d do it anyway.