It doesn't necessarily mean at all that the composer plays his own works best.
But in the end, music is ultimately an aural art, pure and simple.
Of all the arts, music is really the most abstract.
You write it down because finally, when it's written down you do get it out of your system somewhat.
In writing music, the structure of each piece is a very important factor.
A person improvising is sometimes very fortunate that just at that second things coincide.