How clever are dogs?

As is to be expected, we have been trying to teach our 'puppy' (does an 8 month old dog weighing in at 21kgs still qualify as such?) certain things.

1. We have tried to teach her to come when she is called. She comes when I call her. She is erratic in response to the boys and she ignores my husband altogether.
2. We have tried to teach her to sit when she is told. She does this when she feels like it. There are times when it is perfectly obvious she knows what you want of her, but she is opting to decline your kind invitation. I have always felt that deliberate disobedience takes more intelligence than unfailing compliance. I'm just not so sure I like it that much!
3. We have tried to housetrain her. She has realised that it's good to pee and poo in the garden. She has yet to learn that it is NOT good to pee and poo on the lounge carpet. Fortunately, our visits to the back garden are frequent enough that she seldom has the need to demonstrate this ignorance.
4. We have taught her to 'stay' when we put her into her 'bedroom' (the integral garage - don't worry - it's been made over into living space. Like most other people in the UK, the last thing we would think of doing with our garage is parking a car in it) or when we leave the house for a short time.
   
5. We have tried to teach her only to take food when given permission. We're making huge progress here, but dogs are by nature foragers and scavengers so, unless she has been expressly told not to eat something that is conveniently placed within her reach (like on the very back of the kitchen counter, for example), she is likely to be found munching away on the chocolate muffin you were saving for later.
6. We have taught her to give a paw when asked for one. Because this generates a reward, she now lifts her paw without being asked... just in case.

And it's this last point that I've been thinking about. Mark Berthelemy (sort of) addressed the issue of dog training in this post a while ago. What about the things they learn without being taught? How much intelligence are they demonstrating?

For example, I am trying to teach my dog to fetch a ball. We need to be sure of her response to recall before we can take her off the lead in parks. During my all too brief lunch break today, I threw a ball for her, using commands like 'fetch', 'bring', 'drop' and 'leave'. She has a short attention span and I could see that she was bored with this game really quickly. I threw the ball, and yelled "Fetch it!" She did. But when I called "Bring it, Jessie!" she failed to comply. Instead, she took the ball to a corner of the garden and put it behind a bush. She then arranged dead twigs and living branches so that the ball was hidden. When I went to retrieve it, she placed herself across my path so that I couldn't reach the ball. When I reached over her, she (gently) headbutted me out of the way and sat down. Quite clearly, she was saying "Leave it!" to me.

I never taught her that. She has never done anything like it before. The closest she has come was to bury a bone, but that's sheer instinct.

Is this informal, learner driven learning in action? One woof for yes, two for no.