Everyone except Administrators starts off with zero rights to edit channels in Multimedia Manager. Rights to edit channels must be granted by Administrators on a channel-by-channel basis. This is by design so that control over who can edit what is always maintained. That is especially important in a high-profile tool that can be used to distribute content throughout the website and beyond (via RSS).
For more information on how to grant channel access to individual users, see the Knowledge Base article, Editing rights to Multimedia Manager channels.