KG's a self-taught reader ... we taught him letters and sounds when he was very small (he loved it -- his dad would push him on the swing and say "A", KG would say "B!" dad would say "C!"), but he turned out to be a whole-word reader.
Yes, I do think he learned by watching us read. We never pointed at words as we read them, but when he got to be 2ish we'd pause in our reading of familiar books and let him fill the word in from memory; at that point, he'd be following words with his eyes as he read. I think he put the whole thing together, letter sounds to help him out, and just solved the reading puzzle that way.
He's a big-time whole word reader, though; he didn't ever have a "sounding out" phase, which saved him a lot of time becoming fluent and expressive. I've never heard him sound out a word; if he comes to a word he doesn't know, he mentally breaks it into groups and just takes a stab at pronouncing it aloud. But he was 4.5 or so before he started that approach; I think his sight-word box was full! He started reading around 3 and was at fourth-grade level before he turned 5.
Like your son, Erica, he read the same books over and over (lots of picture books) when he was learning to read, which I think drilled those sight words into his brain. And he had several favorites that we'd read every other night or so ("Chicka Chicka Boom Boom," "Are You My Mother," "Freight Train," "Goodnight Moon," stuff like that), so he became very familiar with those words and just *knew* them. In fact, I think the very short and simple book "Freight Train" was the one that made reading "click" for him. Very few words in it, but it really held his attention and he loved following along.
What he does now, and it fascinates me to watch him, when he comes to a word he doesn't know is he compares how it looks to something like a "database" in his head of words he's heard and he works it until he matches them up. I'll hear him sound the first couple of letters to help him decide what word group to start with, he'll say the first few sounds of a couple different possibilities until finally all the blocks fall into place and he knows the word. He never stumbles over it again after that. If the word is just too strange to match up phonetically, he'll come up with some very interesting pronunciations, lol (segue is segoo).
That's just exactly what KG does now, at 6. It's fascinating to watch! And like your ds, once he knows the word, he knows it. I find it so interesting how kids learn to read in different ways. Luckily for us, it was pretty much effortless with KG. I think it would be really difficult to have a child who really struggles with reading.