Check out the ascx file and not that each button has it's visibility. The control definition by default looks like this:
ButtonVisibility-SingleItemView="False"
ButtonVisibility-ShowCopyCutPaste="True"
ButtonVisibility-ShowExtendedCommands="True"
ButtonVisibility-CommandFolderUpShown="view"
ButtonVisibility-CommandNewFolderShown="edit"
ButtonVisibility-CommandNewItemShown="edit"
ButtonVisibility-CommandDownloadShown="False"
ButtonVisibility-CommandCopyShown="edit"
ButtonVisibility-CommandCutShown="edit"
ButtonVisibility-CommandPasteShown="edit"
ButtonVisibility-CommandDeleteShown="edit"
ButtonVisibility-CommandHardDeleteShown="admin"
ButtonVisibility-CommandUndeleteShown="admin"
ButtonVisibility-CommandViewShown="view"
ButtonVisibility-CommandEditShown="edit"
ButtonVisibility-CommandRollBackShown="edit"
ButtonVisibility-CommandLockShown="edit"
ButtonVisibility-CommandUnlockShown="edit"
ButtonVisibility-CommandApproveShown="approve"
ButtonVisibility-CommandSubscribeShown="view"
ButtonVisibility-CommandUnsubscribeShown="view"
/>
You are referring to the last two. The value can be set to True (show always), False (show never), View (for those who can view), Edit (for those who can edit), Approve, Admin. You'll want to set them to false.