Is Telling Always Wrong?

Show, don't tell. If you've even driven past a writer's conference, you've heard this mantra. It's probably the first chapter in every style book ever written.

Show, don't tell, eoooum. Sorry. I hate The Wizard of Oz, yet here's a reference!

Can there be times when telling is appropriate? I was reading a thread on The Anomaly appropriately titled "Show, Don't Tell," and I got the impression - no, it's never okay to tell something.
I disagree. Respectfully, of course.

Yes, telling is overused and can be a sign of lazy or amatuer writing. But sometimes, it is appropriate.
An example: Rhami, my wizard among barbarians from Star of Justice. In the sequel, I have a scene where Rhami is alone and thinking. He's throwing a pity-party, is what he's doing, but he would call it "thinking."

How can you show thinking? I can show what he's doing while he's thinking but what he's doing and what's he's thinking are two different things. I could have him talk aloud to his toad, but that screams "obvious plot device!" And not everyone talks out loud when they're alone. I don't. Rhami doesn't. I don't share my opinions with my critters, either, because they don't care. Why talk to an audience that doesn't listen? Waste of breath.

Some might argue that I have no business having a character think in a book. It's not active enough. Rewrite the scene and get the information out some other way.

To me, sometimes going out of your way to not tell is more annoying than just telling. If you can tell me and get on with it, I don't mind so much. Just don't do it all the time.

Another problem. Jeff the Publisher suggests writing the narrator voice as the same voice as the main character. He admits it's a subtle skill, but what if the main character is an arrogant yet insecure, highly educated wizard who has a habit of bloviating? Won't that come out in the narration? Wouldn't the telling in this instance actually be showing because it shows the character of the character?

If I posted this on The Anomaly, I'm pretty sure I'd get a "good thought, but you're wrong" reaction, simply because, once again, writers are supposed to be endlessly creative and always looking for better ways to show not tell. I agree with that philosophy.

But I maintain that times exist when a little telling is not necessarily a bad thing.

So, are you going to tell me I'm wrong or show me?