Using a highly accurate clock to solve ordering like that is punting on the actual problem. It's possible for requests to different servers to happen at exactly the same time. You need a mechanism to handle that. And any mechanism that can handle that can also handle clocks being a couple hundred milliseconds out of sync.

At a certain level of precision you have to accept that data only travels at the speed of light and there is no way to have a global ordering that shows data consistently and immediately. So you can use an easy non-immediate method like a vector clock.