I agree, and I disagree with their rationale. IMHO, just because every line of code is covered by a unit test doesn't imply that the product is adequately tested. Errors can occur at more systemic levels via integration of well tested components. Furthermore, developers have blind spots and hidden biases and can't fully compensate for the lack of an aggressive QA person who is trying to break your code.
On the other hand, they're clearly doing something right, so far.
I agree with you so much that I wrote a substantially identical response to a sibling comment, with the exception being that I neglected to congratulate them on their success. Clearly what they are doing is working for them right now. I have spent years testing payment systems, and it isn't easy. They must have an exceptional group of developers.
I wish them continued success, but I encourage them to start looking for a rockstar QA/release engineer.
They didn't say that they ONLY write unit tests. They possess an automated test suite that covers multiple levels of application integration and acceptance checking, in which "unit" is only the first line of defense.
On the other hand, they're clearly doing something right, so far.