This really depends on the individual dog, and how they are introduced.
You can't bring a kitten into a home with active hunting dogs. The cat is a prey animal and the dogs are trained to take down prey, so they will kill the kitten. If they don't, they won't be effective hunting dogs.
If you get a cat, and have the cat established in the home, and bring home a puppy of a breed that is not prey driven, then there is a good chance that everybody will get along. The pup will try to interact with the cat, and the cat will either accept it or tell the pup where its boundaries are.
My parents have dogs and cats living together. They had cats for years and adopted a westie pup. She took one wrong look at one of the cats, the cat hissed, and she never got closer to the cat. Even now, years later, she leaves the cats alone. Sometimes they will play with the same toys, but the wesite is always aware of the cat and if the cat is done playing. She is super smart and understands things like that.
So you are right, it is totally possible to have dogs and cats in the same house and have them get along, but you have to do it the right way and have the right kind of dog.