One thing I was never clear on is: does boot0, boot1 happen on power button? Or on power? I can't think of any other way a wii remote button press would start the system.
I can't verify this with my Wii right now because it's standby behavior is... strange. I don't know if it's because I have bootmii/boot2 on it or what, but when it's supposed to be in standby, it instead constantly runs the fan as if it were still on. At some point in the past it worked as I described above though.
Just tested this with my Wii, I put it into standby mode and the Wiimote turns it on.
Another thing is that there are two different standby modes for wii once first booted (can be configured in settings), in one the Starlet is completely powered down (red LED) and in the other it stays on and runs scheduled tasks (orange LED). In early hardware revisions the fan is stopped in the orange mode, while in the later revisions it is temperature controlled (the first revisions will overheat and degrade/destroy the GPU if left in this standby mode for too long).