Like these ones being bred by an irresponsible backyard breeder? Yes.
This is why you need to research your breeder--good ones put a lot of time and money into avoiding inbreeding. They do things like cooperate with each other to 'borrow' male dogs from one another or even going so far as to buy sperm from abroad and have the female artificially inseminated. They also keep careful records of lineage to help avoid accidental inbreeding.
But if you get a purebred from some random person or rescue, then yeah, it's likely been inbred and not had the various health and genetic screenings that you would get from a good breeder.
Edit:
For personal anecdote, I should share that the breeder I am going through for my next purebred puppy thought she had one for me with this litter, but he started developing health problems around 8 weeks old, so she decided she is not willing to sell / adopt him out until and unless he doesn't have any serious health problems. She's clearly very attached to him and it sounds like she wants to keep him regardless. She has already spent thousands of dollars trying to figure out what's wrong with him, including expensive genetic testing.
And this is why the good breeders charge exorbitant amounts for their dogs.
Oh yes, I agree completely. The encouragement of breeding of any brachycephalic traits should be treated as animal abuse. There are other examples, but that's such a big one.
Yep. My mom's Chinese Crested is the result of a mating between son and mother, so she got it for free. Amazingly, she's a very pretty and very sweet dog with no health problems to speak of.
I'm against the whole purbred dog thing, but at least my mom gave one a good home.
They can be, respectable breeders will usually do it outside of their dog's own gene pool (mating them with another owner's dog that has the same desired qualities), but there are definitely breeders that keep it within the gene pool in order to maximize the desired genes being expressed.
To be fair, there's some stuff that was bred into the gene pool near the inception of the breed that can't be easily removed now. You can reduce the risk by avoiding incest and thorough genetic testing where possible, but there's some health issues that would plague purebreds for a long time even if every breeder in the world was responsible.