So you've answered what I've been asking. They only accept knockoffs.
I am betting that there is a lot of confusion about what they will accept and what they won't. I emailed apple's executive team about my issue with apple's service provider refusing to offer the program today.
I would suggest that others who get denied (such as the person trying to use a samsung branded charger) email as well to confirm that it is only pirated or knockoff chargers that can be exchanged and not any third party phone charger. I imagine that there could be some rogue stores that are not acting per the instructions from corporate.
i used the sjobs@apple.com address to contact the executive support team. I have not heard a response yet, but it is Saturday.