Okay, here's where you lost me: "No, crossbreeds are more healthy due to hybrid vigor."
This is an absolutely false statement. A hybrid is NOT the result of crossing two (or more) breeds. It is the result of crossing two SPECIES. And crossbred dogs are NOT more healthy.
What it is, is that knowledgeable breeders KNOW that the marketing of Doodles, Noodles, Orkis, Poos, etc etc is a marketing scam. Because they are NOT what those who breed and sell them (for exhorbitant prices) claim that they are. The "breeders" of these mutts (face it, this is what they are, and I won't apologize to anyone who feels that is a derogatory or politically incorrect term - heck, Obama called himself a mutt...) rarely, if ever, do genetic health clearances on the parents of these crosses, and we all know that Goldens and Labs can have HD/ED, SAS, thyroid issues, eye problems, etc. Poodles can have HD/ED, SAS, eye problems, Addison's Disease, etc. If any of those health issues are present in one or both parents, breeding them increases the chances of the offspring having them, as well. They don't magically go away because they are "hybrids" (which again, they are not).
Part of the problem is that just because you don't look for it it doesn't mean it's not there - and I know of very few people with mixed breed dogs who do health clearances such as hip/elbow radiographs, cardiac testing, or CERF eye checks, and having worked for many years as a vet tech, I'll tell you that mixed breeds have more than their share of health issues that very well could be any of those problems. But without checking for them, they will never know.
Stating that there are a heck of a lot more Golden Retrievers in shelters than there are Labradoodles (or Goldendoodles) would be because THERE ARE A HECK OF A LOT MORE GOLDEN RETRIEVERS THAN THERE ARE GOLDEN/LABRA DOODLES. And anyone who has done rescue will tell you that the vast majority of the Goldens that ARE in shelters or rescue are not the result of reputable breeders, but rather BYB's, HVB's, and mills. And THOSE are the "breeders" who pay little attention to the standard, health issues, and temperaments, but rather worship the almighty dollar.