As an aid to the discussion: my company operates 737 and 767 aircraft on ETOPS. As ETOPs requires backup electical power, the 737 must have the APU operating throughout the ETOPs portion of the flight (not having a backup system.)
The 767 has a backup (hydraulic ?) generator, and thus doesn't need to have the APU operating, but I would assume it must be serviceable. In this case it would appear that the backup generator is considered a viable alternate power source.
In the same vein as the 737 has only one fuel transfer valve, that valve must be exercised (i.e. opened and closed) in cold soak conditions before the ETOPs portion of the flight. As the 767 is fitted with two fuel transfer valves, it isn't subject to this requirement.