Re: "...using methods that can be replicated anywhere on the planet."
The measurement of cesium oscillation can change depending on how high up one is on the planet (due to time dilation effects).
There is no absolute reference frame.
But if we both use the same definition then we can agree that we're measuring the same thing.
When we get different numbers for the same measurement, that gives us data about the difference between our reference frames, itself useful information.