While there is the scent of rodent in the air, is really the difference. I think any of mine would go for something warm if I have a rat thawing in the room, whether a rabbit or my hand or a puppy. LOL
On any normal occasion that isn't feeding day though, anything is safe as long as there is no rats or mice smells. In addition, rabbits are not actually rodents, so their scent is quite different.