True whites are extremely rare. As your research shows, there are two "white" genes; overo and sabino. Both of these give us the markings we label "paint" or "pinto". From birth, horses that are white are maximum expressed white from one of these two genes. Such is the case of Artic White, the best-known all white pure thoroughbred stallion. He is a maximum expressed sabino. Gorgeous, eh?
However, he does not carry the dangers of lethal white sydrome that comes with breeding of frame overos (OLWS). He actually has a little color inside his ears, which gave him registration as a paint as well. The problem here is, he can and does routinely throw spots. So if you like mostly white with some spots he's a great cross, or you want a registerable thoroughbred with color. But if you're breeding this "white" horse to get another white, it's just not very likely.
However, in the case of white overos, which is the other way expressed to the max on the white markings, if you breed two of them together you are very likely to produce a foal who cannot survive once foaled. Look up overo lethal white syndrome and you'll learn about a very sad reason there are few fully white horses born that can survive.
Of course, there are pleanty of horses who go white. This is my friend's arabian stallion, who pleanty would think is white. But, he was born bay, went gray, and now is a bespeckled white horse!
Edited to add...Jen, if the pure white colt you are looking at is a stallion prospect, PLEASE get him tested to determine if he is overo or sabino. Overo could be a huge heartbreak if he puts white foals on the ground. Definately look at the OLWS angle of it. I have a friend who's family has bred performance paints for decades. While she's a bit blunt and direct in emails, she's really all about the accuracy and a great person. I'm sure she'd be happy to answer your questions or give commentary on bloodlines or other thoughts you might be having. We're talking top-dollar barrel and cow prospects. PM me if you like.