My self-taught dd1 really did seem to "just get it".
Of course, there must have been a progression, but besides my knowing that she understood that written words stood for spoken words, I was not aware of any of it. She did discover that she had to slow down and sound out some words, which was infinitely frustrating for her. When she asked what a word was I would ask if she wanted me to sound it out for her (with a finger following a word) or just tell her what it was--I'd say that ended up being about half the time.
Her frustration with sounding words out (instead of recognizing them--or recognizing a set of letters and guessing) peaked until we started reading some simple Spanish books--always something we have loved to do together. She loves that Spanish sounds are nearly always the same with very, very few irregularities. Her confidence grew so fast, and it helped her with her English words as well. She used to get exasperated and not read anything for days and weeks until this point.
Also, even though we did no formal instruction, she picked up reading right "on schedule"--not early and not late, neither precocious nor delayed.
Give me a few minutes while I caffeinate.
I think a lot of kids can teach themselves how to read....its just that you will have to wait for their natural timing and a lot of people (OMG! The schools do this in K!) have troubles with doing this. Not everybody....but it is hard when everyone else is doing it earlier.
My daughter absolutely refused to learn to read. Finally, I decided that she would probably eventually either #1 learn on her own or #2, ask for help.
She learned to read on her own at 7...now....almost exactly a year later, she's reading somewhere between a 5th-7th grade level. And, no, we didn't do phonics or anything like that. We played a few sight word games-- but she seemed to have already figured those out on her own, too.
Her brother (who is 6) is starting to read on his own, too. I just say you have to read, read, read and provide lots of books for them. It also helps a lot for them to have something they REALLY want to read.