This was from Alexander Schrieiner a former Tabernacle Organist extraordinaire via one of my college professors, also a wonderful former Tabernacle Organist, John Longhurst.
However, there are some things it cannot do. Sudden changes in dynamics can be somewhat difficult to achieve, unless you have many manuals! All of the dynamics must be manipulated mechanically through pedals and switches. Other instruments, including the human voice, are more flexible in creating instant dynamic changes and feeling, and yes, sometimes that requires stretching the RHYTHM a bit, and even bending the pitches, and doing other embellishments such as changing the tone quality or vibrato. Have you ever listened to a great a cappella vocal group? Or heeded a little sign called a fermata?
I was taught that RHYTHM (TEMPO mostly) just exists. Once established, the performers must to JOIN it and stay with it. This is true particularly for certain types of music like BAROQUE music or most dance music. Nothing is worse than listening to a group of performers who do not seem to be in sync with each other. Obviously, they are having trouble sticking with the RHYTHM.
But other music can be more relaxed. Take smooth jazz for example. The expression goes, "close enough for jazz." But even when the soloist may be stretching the rhythm, the other instrumentalists are still keeping strictly to the beat. Even when the soloist may take a lot of liberties with the melody or rhythm, their stylizations only work within the framework of the BEAT. The RHYTHM is still of paramount importance.
Enjoy this example: "Here's that Rainy Day," a wonderful old sad love song.