An answer at How smart are rabbits? includes the following quote and reference.
Rabbits also have no or very underdeveloped pain sensing regions in their brains (source):
Even as a predator rends a rabbit limb from limb, the rabbit may not feel much pain at all, at least, not in the manner that we humans sense it. The idea that rabbits experience 'untold pain and agony' during predation, or even during butchering by humans, is not supported by science.
While prey animals are no doubt capable of feeling pain, it is the anxiety and fear that keeps the rabbit alive in dangerous situations. Problem is, beyond a certain threshold of fear, terror can literally paralyze a rabbit, completely incapacitating it. A rabbit’s high-pitched scream is a response to terror (whether logical or not), not pain.
The comment "not supported by science" could either mean, we have never actually done any scientific testing so there for there is no evidence. Or it could mean there have been scientific studies that prove rabbits don't feel pain. Or it could just be some ones opinion.
What is the the science around pain in rabbits as compared to humans?