Can Rabbits really only drop Rabbit's Foot when killed by the player in Minecraft? [duplicate]

I tried to replicate the rabbit foot drops by crushing them and by cramming again and I didn't seem to be able to replicate these results, therefore it must have been either a quirk due to lag, or I must have already had feet in my chest that I didn't remember.

So in summary, rabbits still need to be killed by the player to drop rabbit's foot.