To ring true
Due to poor equipment and the scarcity of precious metals, metal workers of the Middle Ages were not able to produce coins that were uniform in appearance and weight. This situation gave criminals an opportunity they couldn't resist. Thus, when in doubt over a coin's validity, a tradesman would drop it on a stone slab to "sound it." If phony, it'd make a shrill or dull, flat tone in contrast to the clear ring of a true coin. By extension, a story tested and found acceptable is said to ring true, and its opposite, to ring false or hollow.
Most experts agree that the origin of "phony" derives from the Irish word for a finger ring, "fainne," made of gilt brass and used by con artists in the 1700s. These sharpsters would plant the worthless ring in a public place. When a passerby came upon it it, he'd be persuaded by the swindler to pay him for his share in the find of the "gold." Over time, so many victims were defrauded that the word was applied to other forms of jewelry, then to anything fraudulent.
SOURCES: 'The Encyclopedia of Word and Phrase Origins,' by Robert Hendrickson; 'The Morris Dictionary of Word and Phrase Origins,' by W. and M. Morris; 'The Barnhart Dictionary of Etymology,' by R. Barnhart.