Yup, they'll all say that, but you have to look at what it really means. Health checked by a general vet is fine for the basic stuff, but not for hearts. Guarantees? Read them carefully.
You'll also see claims of Championship Lines...this usually means maybe one or two dogs in a multi-generation pedigree were shown to a championship. You want the majority of dogs to have earned a CH. We show, so our dogs can be compared to and judged on the Breed Standard so they look like Newfs and their conformation is correct. A well put together dog from a long line of the same, is less likely to have and throw orthopedic issues.
Definitely, NOT EXTREME. SAS is an inherited progressive disease, meaning that it develops over time and there often are no signs. The later the pups are auscultated for it, the better the chance of a cardiologist picking it up. General vets can and DO miss the diagnosis. I had a pup who 2 general vets said was clear, took her to a cardiologist who heard a murmur then did an Echo Doppler and diagnosed her with SAS.
To increase our chances of sending a heart-healthy dog to its new home, the NCA suggests checking at right around 10 weeks. Unfortunately, that's not foolproof. Some dogs develop it later than that. We see pups on public forums all the time who are sent to their new homes at 8 weeks of age. That is a huge red flag that the breeder is not reputable. EVERY breeding dog needs to be cleared by a board certified cardiologist after a year of age to decrease the chances of passing it on.
Distance one must drive, should never take precedence over doing all you can to insure a pup is healthy. Pups will become family members. Imagine a child completely bonded to his Newf, only to find it dead from SAS at the age of 1 or 2 or 3... I, frankly, couldn't sleep at night, if I hadn't done all I could to avoid that kind of heartbreak.
There are other heart conditions that affect Newfs. The above mentioned pup ended up having a PDA (Patent Ductus Arteriosus), not SAS, which is condition that can be repaired via surgery. Her surgery cost me tons more than I sold her for, but she's living a good long life under a limited registration and was spayed.
You just defined who NOT to go to. Anyone who sells online, without knowing the buyer isn't reputable. Oh, they'll sell you some well rehearsed answers to your numerous questions, which will make you think they're good breeders, but they're not. In the end, they're in it for the money, lack knowledge of issues behind their dogs, and won't be there when problems arise. These are the Newfs that end up in shelters or rescue with health and/or temperament issues.
I can tell you I've never broken even on any litter I've bred... Insuring that we are breeding healthy dogs bred to the breed standard so that they look like Newfs (and, yes, that involves showing) costs way more than one can imagine. Our precious Newfs deserve that level of commitment.
My advice to to drive the many hours it takes to get involved with a regional club and eventually apply for NCA membership. I, too, am very rural and isolated and have to drive long hours, but you gain a lot from being around others involved in the breed. Once people in the fancy, including breeders, get to know you and your level of commitment to the breed, your chances of getting a well-bred dog who you might be able to breed, are increased. Pairing a male with a female is much more than merely "buying a male". You need to match pedigrees and try to offset weaknesses with strengths in the mate. Expect to become involved with a mentor. My mentor had bred Newfs for over 40 years. She knows more than I can ever hope to know about the dogs in the different pedigrees. She can tell me health and temperament issues in lines so that I, hopefully, don't double up on problems. Even then, Mother Nature steps in and throws a curve ball. HEALTHY PARENTS DO NOT GUARANTEE HEALTHY OFFSPRING. This is why you need to know what's in the pedigrees - there's good and bad lurking in the genes in every line.
Newfs are fabulous dogs, but they are not for the thin-skinned. Heartache rears its ugly head far too often. This is why you are hearing what seems like complaints and blunt warnings from various people. No one wants to drive you away or be mean. We love and are very protective of our incredible breed. We want to do everything we can to keep our Newfs healthy and look like Newfs, capable of doing what they were originally bred to do. Those who are on the fringe of the fancy and breed without doing everything possible to achieve this, just simply shouldn't breed.
You sound like your heart is in the right place. Just be patient and take the time and long-term commitment necessary to bring some beautiful, healthy Newf puppies into the world for families to love.
Edited to add the italicized sentences in blue.