They can and do drop dead from fear instantly. I keep angora bunnies because I'm a handspinner, and once came down to my buns (who were locked up at night in a secure, brick outhouse) to find two of them dead. Not a mark on them - no illness or disease. We'd heard foxes - the buns must have, as well. Another time I heard a fox and its cubs making a racket down the side of our house. In the morning I found a very young, healthy looking hare, dead. It had been hiding behind a bike propped against the side of the house.
What you're describing with the wild rabbit is instincts and prey drive kicking in. I'm afraid the fact the dog seemed shocked afterwards is no guarantee he won't do it again. It's hard to train prey drive out. So your job will be to keep the buns secure.
Now, that said...
If your area is fox proof it will hopefully be dog proof. But it might not be.
Our old dog (bull terrier) was utterly kind to rabbits. I have to have them on my knee to groom them and she would sit an inch away, and just ignore them entirely. So when she died last year we got a young, bouncy staffy cross, I was dreading what would happen when we let her in the bottom garden (it's behind a gate and she's only allowed in it when we are there too). As the buns were out in their run. She clocked them; stopped in her tracks and then looked terrified. Even now, she won't go up to them. I still only groom them when she is on a walk or firmly shut in another room just in case. A dog can tear apart a rabbit run to get to a bun - even a foxproof one. I know some Jack Russells who did that, round here.
My other bun is in a hutch and run in the front garden and my neighbour's border collie actually goes up to the hutch to say hello to bun every time she gets back from a walk. And it's not in a "Hello, dinner!" kind of way but a "Hellol old friend" kinda way. So you never know.
The buns I have now seem to ignore dogs. But I have had buns in the past who would be scared.
I would make sure the buns' area is super secure.