What would cause a teacher's media channel to appear in the channel list of the our public media player? I thought teacher media channels weren't supposed to be available there.
Teacher channels (the ones created for them automatically) shouldn't show up in the selection of channels you access via the a public media player. If, however, the teacher creates an entirely new channel, that channel will appear on the Public Gallery, the listing of visible channels. A channel can be removed from the Public Gallery by editing its settings and selecting "No" on the "Display in Gallery" dropdown menu.
Media that is intended for view only via the teacher's website should be added only under their own special channel. That media then should not show up in the channel list in a public player. Teachers should use folders within the channel provided to them to organize their media.