If someone breeds, but doesn't have their dogs in any kind of public arena for scrutiny, I'd be very dubious. It doesn't have to be conformation showing, but I'd want then to be involved with a club and active on some aspect of the dog worls, not breeding litters for sale. That means not just having AKC registration but INVOLVED with with AKCSC or CKCSC (NOT just AKC reg, that means almost zilch). The only exception would be breeders of long standing whose dogs are central to the CURRENT show scene -- having a dog a few generations back that has a champion in the pedigree is a 'so what' situation; almost all cavaliers have champon dogs a few generations back.
I'd be kind of dubious of anyone who isn't showing, isn't involved with clubs, and has puppies available right away. If you are wondering, PM Nancy as she is good at recognising some of the more questionable breeders.
The thing about BYBs and questionable breeders generally is: you want to ask WHY they aren't involved with shows or club activities or dog sports.
I wouldn't necessarily trust the recommendation of a prominent vet who has taken a puppy -- vets often don't know all that much about breeders and breeding -- especially if the breeder herself advertises this on a website as a selling point, as this is the typical thing a questionable breeder will post to make them look more legit. Good health focused breeders simply do not need to make these kinds of statements on a website.
Bottom line is -- if they simply have AKC reg and are not active members of either ACKCSC or CKCSC then I'd be very wary. I'd be very wary of any breeders that are only found by website too rather than from recommendation from one of the two US clubs (ACKCSC or CKCSC) -- my experience is that very few good breeders have websites, and most of those who do have pretty basic sites (with a few exceptions!). The breeders with elaborate websites with testimonies and recommendations tend to be the most questionable, again with very few exceptions -- they are trying to persuade people; whereas good reputable breeders don;t have to prove things by appearance as they can prove their qualities by substance and public reputation. In short: good breeders have waiting lists and rarely have puppies available right away. They are also usually too busy to show pics of all their latest puppies. Their sites tend to be fairly simple. If a site is set up to make it very easy for you to view puppies and buy one, and is mainly focused on selling the breeder and her puppies, I'd be extremely suspicious. I'd be very suspicious of anyone willing to ship puppies without getting to know you, too.
Expect to jump through a few hoops with a good breeder -- personal interview, discussion back and forth, etc.