Explosively loud audio by participant who claims there is no audio setting.

Okay, I'll bite. 

First, good job not trying to resolve it while live if you were not prepared with the answer. Sometimes we just eat it and move on. But...for next time...

Sounds like the individual did not access the audio settings. That would be in the menu to the left of the settings menu in the Zoom application. 

I typically have Automatically adjust volume turned off for Zoom and I always use a headset. Automatically adjust is helpful for open or proximity microphones that people may move closer to and further from or for group spaces that may erupt in laughter or applause. You don't want that on for a headset. With that feature off, use the microphone volume slider to decrease the volume it hears from that mic.

While you're here, have them check to make sure they are on the correct mic and use the test microphone option so that they can hear for themselves that they sound absolutely horrendous. I'd even edit out a clip of the recording of the session and send it over to them to watch - or better, ask for their feedback on how the session went and compliment them on a few responses with time stamp. Appeal to their ego to get them to listen and reap the rewards. 

Okay, that's all the magic I can spare on this one post. Let me know how it goes if you get a chance please. And feel free to refer your friend to us for help. We're really nice, though I may sound like a total jerk based on my above reply.  I've been at this work for a while. Direct, innovative, strategic, but not jaded. 

I guided her into "Settings" and she advised that it opens with the Video settings only i.e. no list of options including Audio; I tried to replicate this on my machine by opening  Video settings and shutting down but the normal page was always there on return.   Someone on the Webinar with some IT background suggested that where part of a menu is missing it's usually a driver error (or maybe hardware - unlikely if error is on two laptops).