What "band of muscle which surrounded the skull" are you talking about?
eMedicine - Scalp Anatomy : Article by M Abraham Kuriakose, MD, DDS, FRCS
Here is an image
of skull layers.
Look up the "galea aponeurotica" layer (otherwise called "Epicranial aponeurosis"), this is the muscle layer. It is very thin.
I don't know where you read that it is 1/4 inch thick on normal people, or that it can be up to 1 inch thick on some people, any source that says this is plain wrong (or they intended this as a joke). These muscles are not intended for protection of the skull, they are intended for mimicry mostly. I can guess one can train them by making faces in front of a mirror, but you will still be unable to build them and increase their thickness any significantly.