there is a difference between purebred and pedigree.
All dogs have the potential to carry genetic disease, pedigree or not. It's just we seem to pick on pedigree dogs in particular because they conform to a type and people are honest about problems that may exist. Buy a mutt and people tend to put the problems down to sheer bad luck in that individual dog, as the rest of the family is know known or heard from again.
As for hip dysplaysia that is a polygenic condition. There are many genes that contribute to it, and it's not only large-giant breeds that can suffer from it. The little ones are not as heavy and hence don't usually show problems. Just like larger dogs can also suffer luxating patellas, something people consider a toy dog problem. HD has also become a fashion to an extent with a LOT of veterinarians giving the diagnosis on sight/touch/poor x-rays. It's still something that needs diagnosing by a specialist vet unless the dog is so far gone like my rottweiler and GSD were.
Heart defects can also show up in any dog, and ear problems in cockers need not necessarily be a genetic 'disease' ... diet and maintenance can go a long way in prevention.
If you do your homework your chance of getting a dog with problems is low. Like I said the people I know with pedigree dogs and mine included, don't have issues. My pedigrees are the most low maintenance when it comes to health. The ones that have had a reduced life span have been poorly bred, yes even the 'purebreed' ones. I know where a few came from and the fact they died younger then they should have was no surprise to me.