I don't know if it's true but someone told me this is the main reason why the likes of Home Shopping Network and QVC keep their over the air transmitters going in many places even though most of their viewers are on cable. It seems like a waste of spectrum space but it's so that they can force the cable operators to carry them.
That's generally not true. US cable and satellite operators are only required to carry the "primary" video feed [1], which is usually the xx.1 channel. In most markets, home shopping channels typically air on subchannels (xx.2, etc.). The exception, of course, would be if the TV station designates the home shopping channel as their primary channel.
Home shopping is usually used to monetize excess bandwidth.
