They have generally been wrong in the past, and I expect that they will be wrong again. Our second obligation is to maintain reasonable and responsible patterns of behavior. There are likely to be some disruptions from the century date change; nothing this complex can be perfectly faultless.
However, we should remember that there have been serious disruptions to service in daily life before, from storms, temporary electrical outages, disruptions of telephone service, etc. In general, these prove to be annoying and inconvenient, but nothing more. Finally, we should all recognize that most systems are built to withstand reasonable service demands.