それで here corresponds directly to the explanation she has just given. So he's basically just confirming what she said. The emphasis is on confirmation, rather than interrogating the reason.

Generally, それで is related to reasons. It can also mean something like 'in that way' as you said, however in this context it's more about why than how. It:s meant to express that you have understood the reason but have some kind of emotion connected to it. For example here he's probably angry/annoyed. It's a subtle expression.