Am I being irrational?

I'd like to share a recent exchange I had with a customer:

1. Customer notes to us that he is struggling to achieve something with our product.
2. We explain that this is currently a limitation, but immediately update & release a new version of the product to help the customer achieve their goal.
3. Customer isn't happy, e-mails us for refund.
4. [This is where I come in.] I ask the client whether the fix worked in an attempt to determine how I can help the customer.
5. Customer says they didn't try it and won't try it, because they don't want to be a guinea pig. Insists on refund, threatens with chargeback.
6. I explain that we released a fix for the problem and hence it's not about being a guinea pig; we're just doing our job & helping them out.
7. Customer ignores last e-mail, rudely threatens to publicize this and again threatens to go the way of a chargeback.
8. I issue refund and at least attempt to explain our actions in this regard & how we actually tried to help. Still awaiting response (if any is going to be forthcoming).