Gifted or just "allowed" to learn?

I read an interesting question online today, "Are children gifted or 'allowed' to learn early?" hmmmm I've been pondering this all day and have some thoughts on how this relates to my family.

The original question was being posed to inquire whether young children are gifted or being taught things by their parents that other parents might not be teaching. Many thoughts about this have crossed my mind today. I thought of those "teach your baby to read" infomercials and how I consider that to be teaching, and ridiculous but let's not go there now. I feel babies should be crawling around and exploring their world, not learning to read.
This led me to think of my son who did not read until he was 7 1/2 years old while at the same time was able to add multiple multi-digit numbers in his head at age 5. He had an amazing grasp of complex concepts that were beyond his years yet none of it was "taught" to him. He just seemed to know things. He had, and still has, a sensitivity that one wouldn't expect not to mention his need for justice and justification. He's very eye for an eye.
This brings me to the youngest of our brood. How much of her language is "taught" and how much of it is just who she is? She learned the entire alphabet in a single weekend by simply playing with magnetic letters. She has the language of a child older than she and yet she's only been hearing since June of 2007, a very short 28 months. So, have we taught her enough language in those 28 months that she's managed to acquire the language of a 4 or 5 year old or is this just who she is?
Of course, there's the first born who has always been a wonderfully talented artist and the second born who has an amazing eye for photography. Those talents were certainly not taught. They just can. So, is it teaching if the child can read or calculate in their head but it's not teaching if it's artisic and they happen to have the natural born talent? Did I teach the ones that did math early and learned the alphabet early but didn't teach the ones with artistic talents?
And, what about the early walker? (the first born, btw) And, the one who was able to play with toys beyond her years because she was mature enough (yes, even at age 2) to not put inappropriate things into her mouth? How about not reading until age 7 but doing math at age 5? What's with the language that should be well beyond the abilities of a deaf 3 year old? (I haven't gone into her musical talents. Another day, maybe.)

IDK, I'm just not buying the notion of "teaching" gifted children the things they know. Sometimes, they just know.