Not always true! Your statement is only true when the running clock's speed is the same as time. Thus, regular time and the clock's time will never meet.

If the clock is running faster than regular time, it will at point catch up to regular time and thus be correct for a split second. If the clock is slower than regular time, regular time will catch up to the clock and the clock will be right for a split second.

If we are being pedantic, running clocks never run exactly the same as time. So they'll be right (very) much more seldom than the stopped clock, which is right twice a day.

If the clock is running backwards at very high speed, it would be right infinitely many times but the proportion of the time that it is right would approach some finite constant.

My girlfriend's microwave-clock runs faster than normal.

Somehow this thing manages to accumulate an error of ~15 minutes in a month.

And we haven't even touched on the issue of 24-hour format digital clocks, which can at most be right once per day if stopped!

The RMS of wrongness of the running clock is probably lower.

> a running clock set to the wrong time is always wrong.

Could be right within 15 min accuracy in the appropriate timezone. And such a mechanism can be corrected for in the postprocessing step.