Right, 12 is 0 on AM/PM clocks. Once you get to understand that, it's easy to reason with (though 24-hour clocks are the far superior siege weapon).
00:00 is not ambiguous, though. There is no such date on 12-hour clocks (there's no zero! Just 12…), and on 24-hour clocks it's unambiguously the beginning of the day (24-hour clocks are zero-indexed).
In fact, 00:* dates are consistently unambiguous, because they don't require you to define whether you're using a 12 or 24 hour clock. I think you're thinking about 12:00 on 12 hour clocks.
00:00 is not ambiguous, though. There is no such date on 12-hour clocks (there's no zero! Just 12…), and on 24-hour clocks it's unambiguously the beginning of the day (24-hour clocks are zero-indexed).
In fact, 00:* dates are consistently unambiguous, because they don't require you to define whether you're using a 12 or 24 hour clock. I think you're thinking about 12:00 on 12 hour clocks.