Yes, they can refuse to sell someone an animal if they have sufficient reason or suspicion. Of course that's at the discretion of the pet store owner.
And honestly, most pet stores (aside from the little local ones) do not care about the animals. Every spiel they have about the animal's well-being is just to lead in to selling you more shit (some of it is legitimate, but some of it is literally stuff you do not need)
Shelters and Rescues are different. A lot of them (at least in my area) ask you a shitload of questions before they will let you adopt. Some of them actually want to see your home and what kind of environment the animal will be living in. When my wife and I wanted to adopt a dog from a local dog rescue, they actually did background checks on me AND my wife.
So, depending on where Chris is getting the cats, they either don't know what kind of environment Chris is taking these cats to, or they just don't care.
Either way, Chris should not be allowed to have cats, and I really wish that Animal Control, who have gotten, what, DOZENS of reports from trolls about the Chandler cats over the years, would take the calls seriously and take those poor animals away from that hell hole