Metrologically speaking, an atomic clock is extremely precise, but we should avoid saying that it is accurate. Take several measurements of the same thing, using the same measuring device. Because of measurement error, you’ll get back multiple values. If your measuring device is accurate, those values will all be clustered around the “correct” value. If your measuring device is precise, then those values will be clustered very closely together.
A measuring device could be both precise and inaccurate if it gives us tightly clustered values that are centered around the wrong thing. “between 8.1462732 and 8.1462735 inches” would be a very precise estimation of the length of a foot, but it would also be a very inaccurate one. Similarly, a measuring device could be accurate without being precise. “Between 11 and 13 inches” would be an accurate estimation of a foot, just not a very precise one.
These atomic clocks are all extremely precise, but are they accurate? Only if they are set correctly. If our newest clock tells us that sunrise was at 2:30:56.8893… in the afternoon today, then obviously it will be inaccurate. Of course, that’s just a matter of calibrating the thing, a task (presumably) easily done. But the purpose of these clocks is precision, not accuracy.
(And by the way, if it were the time of day that we wanted to measure, that is fundamentally an astronomical observation. The Earth’s orientation relative to the Sun is what determines the time of day. To measure that, an instrument inherently more accurate (though also far less precise) than these atomic clocks would be the humble sundial.)
Coming at this from a theoretical standpoint, let’s suppose we have a conventional clock perfectly calibrated as of noon on June 21st, London time. We all agree there’s an error in the clock, albeit a ridiculously small one. Over time that error will accumulate, and the time will drift further and further from high noon. In the case of an atomic clock, that drift would be too small and too slow for us to ever care (within our lifetimes), but compare it to a sundial: so long as that thing stays oriented towards north like it’s supposed to, it will always read noon at noon. Carry that process out to infinity, and the atomic clock will end up very precisely way off while the sundial remains very roughly exactly right.
As I say, from a practical standpoint, atomic clocks are accurate. But the more theoretical perspective points out the difference between precision and accuracy. The great achievement of atomic clocks is in their precision, not its accuracy. Metrologically speaking.
Of a Sphinx Athwart the Evening Sky 