I'm not even sure why you're trying to argue this. It's well established that Time over Fiber is 1-2 orders of magnitude more accurate and precise than GNSS time. Fiber time is also immune to many of the numerous sources of interference GNSS systems encounter, which anyone who's done serious timekeeping will be well acquainted with.
Trying to argue that neutrino experiments use GPS time, because they do?
I’m sure synchronising all the worlds detectors over direct fiber links would… work, but, they aren’t.
Unless you are trying to argue internal synchronisation in which case, obviously, but that has absolutely zero to do with losing NTP for a day, the topic of conversation.