This isn't my department, but I'd assume our servers have accurate time. But I'd also assume Amazon has accurate time, and you say they don't, so maybe I don't know anything.
Then again being accurate to 1ms worldwide sounds like one of those problems that runs up against the speed of light? We don't have atomic clocks like Google does...
Atomic clocks would get you far below the 1ms threshold. I'll rephrase to within 25ms, since that can be pretty acceptable and doable across the internet by just popping up NTP.
Without a synchronizing service, time can't be trusted to be accurate. Time should always (try) be absolute to a global time, and not individual clocks a devop manually put some numbers in for.
Then again being accurate to 1ms worldwide sounds like one of those problems that runs up against the speed of light? We don't have atomic clocks like Google does...