Oh, no need to fill me in on that little secret. I'm the clock operator for Siena's home games, and I certainly try to be fair about it (my thumb never leaves the switch while the puck is in play or the officials are lined up for a faceoff), but certainly, there's always going to be some discrepancy (although I'd say anything over a half second is a lot). That said, the rule is always what time is on the clock, regardless of whatever discrepancies occurred though the period.
Here's a fun one, if we're going to talk about starting the clocks to the 0:00.1 - When does the clock start? When the official releases the puck? When the puck hits the ice? When the players touch the puck? If we clock operators were perfect robots that could flip the switch with exact precision, wouldn't that be an important bit of information?