Having volunteered with a a rescue for several years (and having a rescue boy of my own), I don't think I'll ever get buy a puppy as long at there are rescue dogs in need. Some people just prefer to start with a puppy, though, and I respect that choice as long as they buy from a responsible breeder. One definite benefit to buying a puppy from a good breeder who has health tested and screened out genetic health problems from several generations is that you increase your odds of a healthy dog. And of course if you are interested in showing and breeding, you can't do that with a rescue.
As far as scary stories, well, no, not every rescue story is a happy ending. Sometimes it's a bad match between the dog and family and sometimes problems come up that weren't evident while the dog was in foster care. But most of the stories are good. But there are no guarantees with a puppy, either. If all puppy stories were great, there wouldn't be so many dogs in rescue and shelters. And even puppies from good breeders can end up with health problems - my family got a puppy from a very reputable, responsible breeder. Sadly, she died before her third birthday from kidney failure. There wasn't a genetic cause for it and it was't something that had ever appeared in the breeder's lines - sometimes bad things just happen.
As far as supporting the breed, I think either one does that. Certainly I'm partial to rescue, but I also recognize that breeding has to continue if the boxer is going to continue to exist. The key is to only buy from a responsible breeder. A big mistake people make is "rescuing" a puppy from a bad situation by buying the puppy from someone who is keeping them in bad conditions (or in a pet store). While I understand the feeling that at least that one puppy is saved from poor conditions, giving money to the person responsible for the conditions will only encourage them to produce more puppies who will suffer through those conditions.
It's also possible to do both - get a puppy from a rescue. It's uncommon and you'd have to patient, but rescues do end up with puppies. In the last year, my rescue ended up with two litters of puppies - one bitch had puppies in the shelter and we pulled mom and pups two days later...and then a few months later, we pulled another bitch a shelter and then discovered she was about to deliver a litter. Certainly that's unusual, and we couldn't believe when we ended up with two in one year, but we did have some families on our waiting list who wanted to rescue but really wanted puppies, so we had no trouble finding homes for them. (In both cases, these litters appeared to be full-blooded boxers, and both moms were turned into the shelter with a male boxer.) The more common scenario is older puppies being turned into rescues or shelters - entire litters are not common, but they do happen.
And it's possible to get an adult dog from a good breeder. My parents did that with their current boy - after losing one, they really wanted another boxer but didn't want to go through the puppy phase. They found a very good breeder who had 1 year old from a carefully planned litter - they had hoped to show him and use him to continue their breeding program, but as he grew up, they realized he wasn't quite up to that. They hadn't quite decided whether to keep him as a pet for themselves or try to find him a new home, and then they met my parents who had two boxers before and would provide a great home, so they let him go. He's now 12 years old and has been extremely healthy for his whole life - a product of good breeding, but a few very minor flaws that made him unsuitable for the show ring.