This is a false belief. Bunnies are actually very delicate. They are unable to regulate their body temperature so their tolerance Is around 50-80 degrees F. Having them in a regulated environment is required for bunnies. Bunnies are also prey animals and can fright very easily. Barking dogs, Screaming Chilren, Loud Music, are all things that can frighten a bunny to the point of a heart attack. Bunnies also have very delicate bones, and their backs and legs are some of the most seen Injuries in bunnies. Paralysis can be caused by jumping off of a couch, or being held wrong, being dropped.
Some environmental predators to bunnies
Myxomatosis is caused by the myxoma virus, a poxvirus spread between rabbits by close contact and biting insects such as fleas and mosquitoes. The virus causes swelling and discharge from the eyes, nose, and anogenital region of infected rabbits.
This can be deadly to rabbits.
Rabbit Hemorrhagic Disease (RHD) is caused by a highly contagious and fatal calicivirus in the genus lagovirus (rabbit hemorrhagic disease virus or RHDV) that affects pet rabbits through contact with items that may have been in contact with Infected wild rabbits (ie. grasses, vegetables, shoes, or Items from the outdoors). The RHDV Vaccine Is one of the only vaccines that rabbits will require. This Virus is 99% fatal, and has been seen a few times to have no symptoms. You can read more about the virus on www.rabbit.org/rhdv/
Other outdoor prey for rabbits could be stray dogs, cats, raccoons, owls, hawks, fox, and other wildlife. Rabbits can burrow, but if they are scared they can die quickly from fright.