I can't answer for ALL cats, only mine. The 4 I have now were all ferals that we caught as kittens, tamed, and rehomed them to our home. Yes I know my siggy says I have 5 cats. One died and I don't like to think about it....
Anyway, of the 4 we have, all are well fed. They have access to cat food 24/7. Don't know if that makes a difference or not. Three are amazing hunters! They keep the mice population down, and I haven't seen a rat at all. Of course they'll bring a mole, bunny, bird I'm sure, though I've NEVER seen them with a rabbit or bird!
Two are a year old, and still very kitten stage. Full grown, huge kitties, but LOVE to play! They both enjoy ambushes on the dogs, other cats, PEOPLE, and yes my hens. BUT, they don't use claws. They just jump out and smack when you least expect it. Usually you don't even know they are there behind that bush, or under that hedge, and BOOM, you've been tagged. Then they run in the opposite direction, and turn around to watch. The hens naturally HATE it, and several hens have decided enough is enough, and have turned to attacking the cats whenever they see them. Cats always run away quickly.
As for the laying on the belly, and sneaking up like a real hunter...well Daisy and Palin have that down. They love to crawl on the grass towards the chickens/dogs/butterflies/etc., as if they are on the hunt, but, the only thing they actually kill is the grasshoppers, or on occassion a butterfly.
Sorry for the long story to say... it's possible, but I've not experienced or heard of any neighbors with that problem.