Does a simple, single diode envelope detector function the same way as a product detector does?

Mike WU2D has an interesting series of videos on the simple detectors used in crystal radios.  Mike's videos touch on a discussion that I had a few years ago with a member of the Vienna Wireless Association.  I was describing how an envelope detector uses rectification to recover (demodulate) the audio from an AM signal.  The club member dismissed this explanation and claimed that what really happens is that the diode simply mixes the carrier and the sidebands to produce audio.  He claimed that the rectification "theory" was just a fable created to deal with people who really didn't know how mixers worked.  See:   https://soldersmoke.blogspot.com/2022/12/is-envelope-detection-fable-or-is-it.html

I was kind of disappointed by Mike's videos.  He seemed to take an agonostic position on this issue.  He framed it as "some people believe in the rectification explanation, and some people believe in the product detection explanation." As if both explanations are equally valid.  They are not. 

This morning, I asked AI about the two explanations.  Here is what AI says: 

 Does a simple, single diode envelope detector function the same way as a product detector does? 

AI Overview

No, a single diode envelope detector does not function the same way as a product detector because the envelope detector is a non-linear circuit that recovers the audio from a full amplitude-modulated (AM) signal by following its envelope, while a product detector is a linear mixer that recovers the audio from various modulated signals (including DSB-SC and SSB) by multiplying the modulated signal with a local oscillator. Product detectors are more versatile and offer better signal quality than simple envelope detectors, which are limited to demodulating DSB-AM signals with a full carrier. 

I know that AI sometimes gets it wrong, but I think that on this one, it has it right. 

I don't think it is necessary to include discussion of modulation percentages nor diode biasing to clearly explain what is going on. 

Even if you are using a very weak signal and are completely in the square law region of the characteristic curve,  you are still essentially dealing with a form of rectification:  portions of the signal on the positive side of the curve will experience less attenuation than signals on the negative portion of the input curve.

When we use a crystal receiver, we are relying on the rectification done by the diode -- even if the rectification happens in the square law region.  After the crystal there is some low pass filtering.  The envelope of the AM signal remains and this is the audio signal that we listen to.  That is why we call it -- correctly -- an envelope detector.   And as the AI says, an envelope detector funcions differently than a product detector.