No worry there, they don't eat more than they can stomach. When one of mine finds a piece I give it something they like, like some pellets, just because I fear they could feel like when I eat too much raw onion, but that's just my imagination, the rabbits don't care, they wouldn't eat it if it made them feel bad.
It's not poisonous to rabbits, not in amounts they eat anyway. The greens of allium plants can be fed anyway, they are a preventative against parasits like coccidosis.
Dogs are very different animals, they did not evolve to survive everything botany throws at them.
I reckon one can get pretty paranoid when reading too much on the internet...