Follow up. I went back into the store. They said they will ship them in. Apple service treated them like they treated me. Shipped them back and said there is no problem. They looked at them when they got them back, and clearly saw the problem.
SO, the store replaced mine. Went home, charged them up. Synced them with 1 laptop. All was well.
Synced them with a 2nd laptop because I have 2... KA BOOM. Now they are broken again. Resets don't work. The only option I have is to get them replaced a 3rd time, and only sync with 1 laptop because clearly they have zero intentions of recognizing this problem. And I'll look into alternative earbuds for the other laptop and possibly for the future as a whole.
Does the flashing bother me? No not really. Does the fact that it it constantly drains the battery of the case and will shorten the life of these expensive products. Absolutely.