"That isn't ADD, it's being bored"
I think you miss the point. The point is that one task cannot take up his entire attention (the ability to focus).
I've never been DXd with ADD or ADHD -- but I am aspy. I similarly had the issue described above. However, I found my work-around was to have the TV playing in the background or listen to an audio book or music while I did homework. It needed to be something I was already familiar with so it wouldn't draw too much of my attention. That way, the part of me which WAS working on something that needed to get done wouldn't get bored or become easily distracted.
In class, I had a number of other "work arounds". I would "ignore" the teacher and work on another subject while they lectured (if it was material I could get from the book). Or I might find something mildly entertaining to think about (for me it was reciting Monty Python sketches in my head) if I needed to focus on the lecture. I found I could also focus better without distractions when taking notes if I used multi-colored pens and categorized sections by color.
My understanding is the ADD/ADHD crowd could NOT really adapt the way I could and as I've gotten older, I've been able to wrangle in the various "bubbles" of attention in to problem solving groups without needing to "trick" myself with outside diversions.
One of my earliest memories from elementary school (probably 2nd or 3rd grade) was when I was talking with a class mate and the teacher interrupted me and asked me to repeat what she had been saying. I went on to repeat everything she said for the last 5 mins. She was an awesome teacher -- She got me. She explained to me that while *I* could pay attention while doing other things others could not and I needed to find something else to do that wasn't distracting to THEM.