Oh, but the age disparity is precisely what makes this methodology so useful. Globular clusters have the OLDEST stars in the galaxy. They look at the oldest stars in the galaxy, and then looked for the faintest white dwarfs among them (meaning the oldest of the oldest, so to speak).
Thus, the age of the oldest visible white dwarf defines a lower bound for the age of the Universe. To this age (12.7 x 109) they add a billion years, which is the minimum estimate of the length of time it takes for stars to form AFTER the Universe started. Thus the minimum age for the Universe is 13.7 billion years (+/- 0.5 billion) by this method.