From Clocks, a brief and picture-heavy book by Simon Fleet:
Small water-clocks were used in the Athenian Courts to limit the time a lawyer was allowed to speak. This led to those who filled the water-clocks being bribed by lawyers to fill only partially the container when rivals were pleading, and so reduce their opponents' allotted time, and the same thing used to happen in Rome under Pompey. There is a story that a Roman prisoner's life was saved by a pebble falling into a water-clock, which made the water drip so slowly that it gave extra time for some delayed evidence to arrive, which acquitted him of murder.
As Fleet notes elsewhere in the book, the timing of things down to the minute wasn't considered a necessity until the rise of the railroads in the nineteenth century. Up until that point, clocks were mostly considered a luxury. But duration, at the very least, was important in some respects, as in the Greek and Roman court systems. Perhaps it's not too surprising that the clocks of the time were sometimes used and abused in corrupt ways. Of course if you were an innocent man on trial for your life, you wouldn't object to their being a bit fallible.