Is it really true that fixing your pet prevents early death?

Vet’s are always saying that if you fix your pet they will live longer healthier lives. Funny thing is every time I hear of a pet who got fixed they died of some sort of cancer at a young age. Where I have known a few who were never fixed and died at a ripe old age. So is it just a coincidence? So yes if your dog gets his testicals cut off he won’t have testicular cancer, but there are a lot of other illnesses that kill. Whats to say that by messing with your dogs chemical balances you don’t upset the apple cart?
If a woman goes through a hysterectomy a host of health problems happen. So wouldn’t it stand to reason that the same happens to your pet? I’ve seen pets who have gotten fixed suddenly go from being vigorous to being lethargic. True it doesn’t happen to all but I’ve see it happen to a few. I’m not advocating not neutering your pet but simply wondering if there is a down side to fixing your pet that no one ever discusses simply because they are not human.