Age of universe vs. age of stars

There was some dispute not too many years ago about the age of the universe
based on observations about expansion rate of the universe vs. the age of
the oldest stars known within our own galaxy (or possibly within other
galaxies too). Specifically based on expansion rates, the universe should be
around 15 billion yo, whereas based on the oldest stars the universe should
be at least 20 billions yo. Has that dispute been resolved? I presume one
party or the other has been proven wrong, or backed down on their assertion?

Also if this debate hasn't been settled, it is possible that they are both
right in a sense? What I mean is, is it possible that the oldest starts can
be over 20bn yo, but the edge of the _observable_ universe only goes back
15bn years? That is to say that there is a larger universe out there that is
expanding away from the rest of us at speeds greater than the speed of
light, therefore light from there would never get a chance to catch up to
us? The reason I say faster than the speed of light is because General
Relativity prevents matter or energy from travelling faster than light
within space, but it puts no speed limit on the rate of expansion of space
and time itself.

Yousuf Khan