If this were true, then why even bother to make atomic clocks? Why would an article about the "most accurate clock" be interesting to smart people like HN readers if there's no objective measure of accuracy (or if it didn't matter)? The correct answer is in a sibling comment to yours: we base it on other things we know (or believe, anyway) to be constant.
I'm fully aware, but you seem to have misinterpreted what I was saying.
If "all the clocks are wrong" it doesn't matter as long as they are consistent. (in the case of atomic clocks, frequency of energy transitions within atoms)
All ntp servers get the average of atomic clocks, which is then distributed to all phones and computers.
If the constants from these atomic clocks "are a little bit wrong" it does not matter (for most human activities)
That's why we average them and distribute the average.
For physics related research, this new clock being more precise does have use, but for pretty much everything else, whatever constant we have is good enough as long as it's consistently used.
Back in the day it was someone just running around with a pocket watch giving everyone the time from the clock tower which was calibrated from a sundial and that was good enough.
Replace the sun's shadow with electron transitions and the timekeepers with ntp servers and that's what you have today.
