Even if you find out that your son does not have ADD/ADHD, you can still use some of the useful techniques that I find work with kids who have those diagnoses (I have 1 with ADHD and 1 with ADD - one is on meds for ADHD one is on meds but not for ADD). It seems like his brain is "atwitter" and he is having trouble with the "butt to chair" concept. As a veteran of both of these issues :) my suggestion is to handle how you give expectations and instructions a little differently. I will give you an example of what I do:
Dinner time: Before we start dinner, I explain what the "rules" are during dinner - no leaving the table, no bothering others, etc (or whatever your rules are). When I explain the rules, I put my face very close to theirs and cup my hand underneath their chin and we have to make eye contact while I am explaining the expectations. Then I have them repeat what I am expecting. I end this with the consequence (if the rules aren't followed, you will/won't get X).
Instructions: I will use the technique for giving two/three step instructions the same way as above (close face/eye contact/etc) and then I will say "what am I asking you to do?" They repeat it back and then I end with "you are only to do the two/three things I asked you to do. I expect that you will not (stop, play with something else, etc) until you have done exactly what I have asked you to do. Do you understand?"
I know that this seems like a very "dumbed down" approach, especially given that your child is very bright. However, focus for some kids, has to be learned and can be challenging. By making it as easy and error free as possible, you are increasing his chance to learn focus.
I will second other's opinions about the vision testing (many kids have been accidentially diagnosed ADD/ADHD when it was a vision tracking issue) and also having an OT evaluation (not through the school). There are left brain/right brain issues that can be addressed successfully through listening therapy at OT.
Finally, if warranted, don't write off the value of medication. There are a number of folks who do not believe in medicating their child and to each his own. However, as a mom to a kid with ADHD (very, very severe), even he will not miss a single med because he knows how he feels/behaves without them and doesn't like it.
Good luck!