No, it's a service, provided by Square, that you pay for.
Whether Jason is at fault or not, he's disgruntled and public. That's never good news, especially with companies who deal in something as sensitive as payments. Square built a great product, but they are in a very competitive space.
Just because you pay a company doesn't mean you have an unconditional right to do anything you want with a company's resources. You do not pay for unconditional money from customers via Square. Part of what you pay for, in fact, are the resources Square requires to defend disputed charges on your behalf. Part of what you agree to when you join Square is to comply with chargeback procedures.
You pay for the service, yes. You also agree to operate within certain parameters, and don't have a right to demand anything you want just because you are a paying customer.
This seems to be a common fallacy on HN - that any paid customer is deserving of bend-over-backward support, even if the payment amount was less than $1 - Square's net revenue from this transaction.