For those anal about clocks when one is around, it HAS to be accurate (I'm one of them). ANY battery operated clock is a total cr@p shoot as to how accurate it's going to be. Those xtal references are made by the tens of millions and if not trimmed in will NEVER be accurate. Some are dead on, some not, and you never know.
If you want something accurate, get something that says it references WWV, WWVB, or just says "Atomic Clock". An old fashioned analog or digital plugin clock will likely be as accurate since its referencing the 60hz in the house which typically is very stable.