The hardware providing those nanoseconds is not nanosecond accurate (unless using atomic clock)
However they may be more accurate than 1ms. The guy is saying the timeslice given by the OS for a program to run in has at best a 1ms slot because the OS is switching between threads on a 1ms timeslice basis
So unless you're polling, the timing at which you ask the hardware for nanoseconds will jitter with 1ms offsets