I think the main reason why some people say that is because show breeders show and finish most of their dogs before breeding them. They really know their lines and the health of the dogs of many past generations so that health problems are not passed down to pups. Also, the dogs that they breed are within standard, obviously, as they have been shown, most of the time.
I'm not saying that show breeders are the only ones that do research into their dogs lines and such, I'm just answering your question. I know of several non-show breeders who also do research into their dogs' lines and get to know everything about where their dogs came from so that they know what to expect out of future litters. There are many reputable breeders that are not show breeders as well.
Hopefully someone else can answer your question a little better
I don't think that simply having champion bloodlines somewhere in the line makes the pups any better. That champion dog could have been bred with an out of standard dog that could be carrying genes for things such as liver shunt, legg-perthes, etc. Basically, just because someone states champion bloodlines doesn't make the dog better, in my opinion.
If you really want a dog from true champion bloodlines, then buy from a show breeder. If it's just a pet and it doesn't matter to you, then it doesn't matter.