I think you can easily get within a few tenths of a second using the setting of the clock via commandline using a script. If you measure the responsetime of your connection you should be able to sync the time to within a few hundredths of a second compared to your reference pc. You'd need to do this quite regulary to compensate for drift however. If you need the accuracy to be very high you might just wait for NTP insted of hacking your own solution together which would just recreate the functionality
A quick qoogeling reveals NTP usually is within 10 milliseconds over the "open" internet and can go down to microseconds using a special kernel and a local time reference as well as a stable oscillator.
This can get as complicated as you'd like, especially in a research environment
I'm pretty sure the cameras systemclock is only used for timestamping your saved videos, so +/- a few seconds should suffice there.
EDIT: if you
really need precision, maybe look into
PTP instead of NTP