I have heard that the way they would prove it was to put the cat in an enclosure and drop in a rodent.
If the cat quickly caught and killed the rodent you had your proof.
Sadly later this became something of a sport with people making wooden pens and dropping in a number of rodents and then dropping in either a cat or dog to see how quickly they could kill them.
We had a cat and three of her kittens when I was growing up. Old house. Mice are still a small problem in the winter. Anyway, the mama would be lying on the kitchen floor, washing a paw to wash her face, and a mouse would shoot out under the basement door and across the room, into the rest of the house. She’d just stop washing and watch it go. She was an *excellent* huntress, but maybe she thought there wasn’t any sport in when they came right on inside. 😁