Agreed, ichtb. It's really insulting to think that people are stupid enough to be taken in by any of this. Anyone knowing anything about dogs knows what they are buying, and responsible newcomers to dog ownership will do their research.
MissA 
DillytheGardener, again, it comes down to knowing what you are doing. If you buy a first generation crossbreed you won't get a non-allergenic coat. If, OTOH, you go for a 3rd gen or higher, and if you have the sense to see the parents and choose the puppy carefully, then the chances are very strong that you will.
The nature/nurture debate around temperament is as fraught with dogs as it is with people. There are no guarantees there either, whether you get a so-called 'pure-bred', a cross or a mongrel, and in any case much comes down to the owner and how the dog is trained.
Can you suggest where a potential dog owner could go to get a mongrel? Someone who doesn't want a rescue dog, but a puppy that they can train themselves, and who doesn't come with the potential to have behaviour problems caused by irresponsible owners, that is? If you can, I will happily pass this information to my son and DIL, who are considering dog ownership and are still at the beginning of the research stage of their search.