Just got off the phone again. Called the "Ben Hill" number in the thread listed above. Finally got a straight answer. She said that all stores will honor manufacturer's coupons (Milwaukee, DeWalt, etc) for specific items, but that when it comes to store coupons like the HF coupon, it is strictly up to the store manager.
I asked every single manager why they wouldn't take it when other stores would, and none of them told me that it was up to the manager's discretion. I guess I'm out of luck because none of my stores are near a Harbor Freight.