It's true, see the David Wineland interview:An interesting observation and I think true, (but don't vouch for 30cm being enough).
"But nowadays the precision of the clocks is such that we have to worry, when we compare clocks, if one clock in one lab is 30 centimeters higher than the clock in the other lab, we can see the difference in the rates they run at. And this is an extremely small effect that we haven't had to worry about before."
No. It depends on gravitational potential. This varies with altitude, but I couldn't see any mention of sea level in the official definition. The pendulum clock is unlike other clocks in that the local slope in gravitational potential determines the clock rate.It like 200+ years go when the second was defined by pendulum clocks - They did not specify the gravity strength they were to run in. Do we do that now? - Tell what gravity strength is associated with the number of cycles that are a second?