I can't recall the google settings screen but you can review everything that google has picked up. I reviewed mine and while most were ok there were a good number of private conversations with my wife that google had randomly picked up. Most of them sounded like stuff I was saying while driving. Which means that it was purely based on what android thought it had heard vs any manual input. I can only assume google home will have similar moments.

Go to https://myaccount.google.com/data-and-personalization

then click on 'Audio and Voice Activity'

How else would it catch the words "Ok, Google" in the first place?

All these things have dedicated low-power hardware that just listens for the trigger phrase and has no network access. That's why you can't choose your trigger phrase.

offline (on device) model for that only instead of cloud based. I'm a deep learning researcher, and that can be done for sure

Just don't enable "OK Google", it's really not that useful anyway.

You should be able to see the services (daemons) in Developer mode.