Attached to the back of our house we have a fenced area for the dogs. We have a bumper crop of rabbits at this time in all sizes - full-grown, mid-size and little fluff buns. At any given time there are 3-5 out in the yard (other side of the fence) munching on delicious grass and clover. The dogs will shoot out of the house to see the bunnies. Sometimes they bark at them and other times they sit quietly and just watch. When the dogs first come out of the house, the rabbits will shoot off in different directions into the woods. Eventually they come back and resume eating not bothered that there are 3 large dogs watching them or even barking at them. They apparently know that they’re safe where they are. The fenced in area is half wood chips and half sparse grass that is continually peed and pooped on. (I pick up poop at least three times a day!)
So riddle me this. When the dogs are in the house, why are the rabbits continually coming under the fence into the dog’s area? I have to go out and shoo sometimes two or three rabbits out of the fence before I can let the dogs out. This is during the day and when it’s dark. There’s nothing in there worth risking a life for. Just pee soaked grass.
One day I was in the house and two of the dogs were outside. I heard through an open window the crying of an animal. I thought it was a baby bird. I looked out the window and couldn’t see the dogs. I went running outside and there they were licking and nosing something. It was a tiny baby rabbit. I cannot believe they didn’t kill it just by playing with it. I picked it up and brought it out back. It hopped away so thankfully they hadn’t hurt it.
I guess I’m just assigning too much intelligence to rabbits! 
The stupidity of rabbits can scarcely be overestimated.
They’re rabbits. They’re walking food for almost everything that eats other things. I suppose they just figure anywhere is as good as anywhere else.
Rabbits are very rabbity.
A few years ago the rabbits around us had a very good year, reproductively. There were rabbits everywhere. My gf put up temporary fences around some of the rabbit nest areas, and bought food for them (fresh greens).
Nature being what it is, we had lots of hawks the following year.
ETA: rabbits are crepuscular.
“The grass is greener on the other side of the fence.” It’s a cliche because it’s true (even if it’s not objectively factually correct in every situation, like your sparse dogpatched grass).
Besides, I seem to remember that the salts in urine can make grass more attractive to grazers.
This is what I was going to say. There’s nowhere outdoors that’s really safer than anywhere else for them, so they rely on their eyes, ears, and ability to quickly hop away from (most) predators. That plus their prodigious reproduction habits keep their species alive.
I don’t think that’s actually true. The original poster’s yard may be safer, simply because their dogs discourage some predators. I don’t think the rabbits are smart enough to think that through, but the simple fact that there’s a lower death rate in the yard means more rabbits end up in it.
That assumption is a bit of a leap. The OP is saying the bunnies are dumb for being in the OP’s yard because the presence of the dogs makes it less safe for the bunnies. True, the dogs may be keeping other predators away, but If I’m in the woods and find myself surrounded by bears, they may be keeping the wolves away, but that doesn’t mean I’m safer with the bears around. The old aphorism "out of the frying pan and into the fire’ comes to mind.
Yes, the OP did say that the dogs played with a baby bunny without harming it, but that’s probably because the baby bunny made no attempt to escape, so the dogs’ predatory instinct was not triggered.
Our wild rabbits are extra dumb. They hop right into the electric wire around the garden. Get loose and do it repeatedly.
Sometimes you can smell hair burning.
I occasionally root for the poor thing to get through. Seems it’s paid the cover charge!!
For me, I’d apply a Darwinian solution to improving rabbit intelligence.
Don’t get me started…
And where are the bunny and dog pictures?
I had a Jack Russell terrier growing up. She caught rabbits in the yard all the time. Killed the crap out of them. She loved it.
Ever seen the video of the terriers on a rat hunt. They kill clean and quick.
I had a Rat Terrier who would kill rabbits like that.
It was awful to watch.
But I just couldn’t get her to stop.
She had a job to do, in her thinking.
She also had a barn job with rats. Some nearly as big as her. Never you mind, if her eye saw it they were goners.
Not dumb, suicidal.
I went out the front door yesterday morning and startled a rabbit, which panicked and tried to race in three different directions simultaneously before darting into the shrubbery.
Thankfully for my garden, local coyotes seem to be keeping down the rabbit population.