More details of how Ooma works are coming to light. Andy Abramson got part way through the install, and then chose to not continue because by agreeing to the Ooma terms, he was allowing Ooma to reconfigure his phone service. A number of folks I've spoken with have also reported the same. During my conversation with Ooma founder Andrew Frame he mentioned that they "stripped away" all the phone company features, which I didn't dig into further at the time. .
That reconfiguration may be a clue as to how Ooma provides some of it's capabilities. Some of us, for instance, have wondered how they're able to correctly show caller ID on an outbound "shared termination" call from the Ooma device. If Ooma were actually a carrier as well as a device manufacturer, that might answer the question. Needing to keep a carrier network running might also explain why the price point of the device is $400.
Pure speculation, of course. For now, the details of how Ooma works remain a mystery.