I've been running a casual experiment that proves your argument. Rode started marketing some audio equipment as eliminating microphone "clipping" through 32-bit float. I've written stories here, done YouTube videos, explain why that is scientifically/factually impossible (with today's microphones and electronics).

I was even kicked off "Audio Science Review" forum.

So a part you didn't touch on is that people generate more lies from their belief system. So in the case of the abused women, they probably come up with more reasons why things didn't happen or weren't important.

In my case, they will argue that using four analog to digital converters (ADCs) they can split the signal into four parts. They don't reference any scientific or technical literature. They'll reference a drawing from some marketing literature.

I'm going to try your idea going forward. Try to boost their confidence that being wrong about 32-bit float is a small price to pay for what they can gain.

We'll see ;)