Yes it's true. At 3 years old, it's very probable there already are tumors forming in her uterus. She's not too old to be spayed (the 'too old' would come from the risk of the anesthesia who is related to the general health of the rabbit - at three years old, she should still be in good health so with a competent vet the risk is really low, around 0.5% and linked to heart problems in most cases) and definitely not too young, as most does are spayed around 8 months old. The 50 % of risks of cancer increasing to 80% around 4-5 years old comes from very serious studies. The reason is obvious : contrarily to other mammals, rabbits don't have 'heat', they are sexually available all year, which means that female rabbits produce an insane quantity of hormones all year around. Rabbits aren't built to live long but to reproduce as much as possible in a short amount of time, which is related to their living conditions in the wild (where they live an average of 18 months).
It was confirmed to me by my vet who is one of the two best rabbit specialists in France. And I've met countless people whose unspayed female rabbit had ovarian / uterine cancer or mastitis. By the time you see signs of it (generally blood in the rabbit's urine, swollen red nipples producing pus) the rabbit has to be operated anyway and her chances of recovery are a lot lower (not even talking about the fact that the cancer could have spread).
Never see that vet again, he knows nothing about rabbits.
With the other, ask how often the he spays rabbits. Ask if your rabbit should come on an empty stomach for the operation (the answer is NO, if the vet says yes, don't let him touch your rabbit) and which method is used for the anesthesia (gas is best for rabbits). After the operation, ask for Metacam and antibiotics for 5 days if they are not given to you and make sure your rabbit got an injection of both before leaving the vet as a rabbit in pain won't eat and you might find yourself with a case of GI stasis on your hands.
