They can't be. This is the fundamental feature of an evolving universe that everyone, even non astronomers, implicitly believe in. The child cannot be older than the parent. The reason such contradictions appear is not 'in the stars but in ourselves'. There has always been a generally accepted broad range of ages for the universe extending from as short as 8 -9 billion years to as much as 20 billion years. These estimates stem from the predictions by a variety of versions of Big Bang cosmology whose key observational parameters are 1) the Hubble Constant, 2) Omega...the ratio of the observable average density of matter in the universe to the critical density set by Hubble's Constant and 3) The assumed value, if any, for the cosmological constant. These three constants are not known to better than about 20 percent, a factor of 10, and a factor of 100 respectively. This means that theoretical predictions for the age of the universe are held hostage by poorly determined observational parameters.
Recently, stellar astronomers have pretty well established that the oldest stars we know about in several old globular clusters, have ages from about 10 to 17 billion years, with several clusters having ages from 14 to 17 billion. No reasonable modifications of the theory of stellar evolution, or recalibrations of the distances to these clusters would reduce these estimates substantially below 14 billion years. Meanwhile, measurements of the local value of the Hubble Constant using the Hubble Space Telescope, now seem to favor values for H near 65 kilometers/sec/megaparsecs. To convert this into an age for the universe,m you also need to know the value for Omega and the cosmological constant, neither of which are known very well, so some astronomers ASSUME that Omega = 1.0 and the cosmological constant equals zero. This leads to ages for the universe that are smaller than the ages for the oldest stars. Other astronomers take the data at face value and argue that Omega = 0.1 and the cosmological constant also equals zero. This leads to cosmological models for OPEN infinite universes with ages that are completely compatible with the oldest star ages. Still other astronomers propose Omega = 0.1 and the cosmological constant has a small non-zero value. This leads to universe that can be handsomely older than even the oldest stars.
So you see, there is more to the controversy that just 1) the deduced ages for the oldest stars and 2) the value determined by the Hubble Space Telescope for the Hubble Constant. This is hard work, and before we really can figure out what the age of the universe is, we still need to tie down Omega and the cosmological constant. Neither of which the Hubble Space Telescope will be able to do alone.