Okay, you've got it a bit backwards; Let me explain.
An Open Differential has what is commonly referred to as "spider gears". These in combination with clutch packs allow one wheel to apply more torque or rotate quicker for better traction so your wheels don't bind up during sharp cornering or if you lose a lot of traction to one tire.
A Closed Differential is locked in place so that any axle or wheel gets the same amount of torque applied to it; These are common drag racing setups since cornering isn't really vital.
As far as your Drive Tire being the reason for wear on the tread.... not likely. I've never in my life heard the term Drive tire used the way you described it. It could possibly have been a VERY misinformed individual that had no idea what he was talking about. Older Honda's did have single wheel drive transmissions, but definitely not an '03. I know this because I worked on their transmissions regularly for years.
It could be possible that someone modified it, but doubtful.
A test you can do is put the car up on a lift (SAFELY). Start the engine and put in Drive or 1st gear. Once this has been done, use a long handled pry bar to push your caliper into the closed position. PLEASE be very careful when doing this!!
The results should be as followed:
- If one wheel stops but the other keeps spinning, you have an open differential.
- If you stop one wheel and they both stop spinning, or you stall the car; It's a closed or sometimes referred to as a modified "welded" differential.
- If you see that only one wheel moves, you have a single wheel drive-line.
Please do not try to hold the wheels with your hands, you will not have the strength to stop the wheels and you can get caught up in something. By engaging the caliper with a pry-bar you're basically hitting the brake pedal without your foot.
This is also very common practice to weed out wheel bearing problems.
Your issue is most likely suspension or subframe related.
Hope this helps!