Weber speculated that the safety concerns may result in regulators restricting the 787's ability to make long flights over water, a standard known as ETOPS.
Is ETOPS dependent on starting the APU? I don't think so, as dispatch with an inop APU is allowed (or so I've been told).
Battery capacity doesn't extend the range of the aircraft. That is done by the RAT (or APU, if it starts). The primary battery serves to provide short term power while the RAT deploys to keep critical instruments powered. And it provides emergency braking power, which is not an ETOPS range issue.
The battery function is binary. It either works or it doesn't. And the trouble it causes by not working is not range or capacity dependant. If the primary battery isn't there upon main power loss, the ensuing problems occur immediately. Not after 90 or 120 minutes. So a main battery failure will affect any length of flight or diversion capabilities.