Hardly. A star that is a red dwarf in stellar metamorphosis theory is quite young, as it is still very hot. The old stars are cold, rocky worlds. Earth itself is an ancient black dwarf, about 3.5 billion years old that we are aware of... it might be a tad bit older. So to say a red dwarf is twice the age of the Earth is clearly very, very strange.
I have drawn up a simple diagram that overviews where a star fits in its "age".
The stars move down the Hertzsprung-Russell Diagram as they cool and die... unfortunately the dogmatists forgot half of their graph, so I added it with explanation.
Or a graph with the ages attached. Notice how red dwarfs are WAY younger than Earth type objects. It is very simple to understand. Planets are ancient/evolving stars.