For some time I plotted the jitter of reception of DCF-77 (a similar transmitter in Germany) and I found there was a clear cycle of increase and
decrease of the jitter of the pulses output by my receiver (measured over one minute) over the day.
At daytime the jitter is around 20us, at nighttime it is more like 200us.
This is most likely explained by path length variations that apparently are depending on propagation.
(although texts about such transmitters often boast that there is no propagation effect like the one seen at shortware at those frequencies)
The claimed accuracy is of course at the source, and maybe when you started receiving WWVB years ago and perform some kind of averaging
over a long interval, you could eventually get an accuracy like that, but there is no way it can be achieved over short intervals, let alone for
individual second pulses.