When a bone is selected in the viewport, selection is also synced with the dopesheet animation channels, but not the other way around. So, selecting a dopesheet channel does not select the corresponding bone.
I've noticed that this only happens with bones. With Objects, selection is correctly synced in both ways.
2_ Channel renaming
It seems that renaming a channel in the dopesheet does not sync its link to an equally named bone correctly...
Furthermore, if you already have keys in a channel, and you rename it with the name of another bone and then you add keys to that bone, you end up having a channel that contains the animation data of both bones. I also noticed that the channel list allows channels with the same exact names....
- To Do
For a long time, I've been marking reports like this as "todo" (for the purposes of tracker management).
That's because, strictly speaking it was never intended that "group channels" = "bone channels", even though that's what they are used for most of the time. Hence, these types of syncing behaviours really weren't meant to work.
I've now marked this clearly on the publically visible "Todo List" on the wiki.
Closing for now, but this time it really is on my todo pile :)