I've read in a few places that a Union Jack flown upside-down had at one time signified a distress signal for hijacked ships at sea. Is this true and has it ever been documented?

This is definitely true in the United States, and it appears to be true for the United Kingdom. In 1791, Vice-Admiral Arbuthnot, the British Commander-in-Chief issued a statement (as apart of a longer list of signal protocols) saying, "When any ship is in distress she will hoist her Ensign, Union downwards; but if she wants immediate assistance she is to make it known by the Ensign, Union downwards, and a white flag under, at the main topmast shrouds." So, we at least know that at one point the UK did employ this strategy.