This is a symptom of a BUG (ok, perhaps a lack of feature) in the 622 (and all Dish HD receivers.) What they *don't* do is what is called Native Passthrough. If they did that, they would send the signal to the TV that is coming from Dish: a 480i signal for SD and a 1080i (or 720p) signal for HD content. This has been a promised feature upgrade for months from Dish, and if/when it comes, it should solve this problem. Instead, as you noticed, you have to tell the receiver what resolution to output (for HDMI and component - your HD outputs).
My solution is exactly the same as Cokeswigga's. I have the Sony KV36XBR (4:3 tube) Use both the S-Video and HDMI (or component) output to my TV and switch the TV's inputs. It's a pain, but mitigated by my Harmony 720 remote - I have a button called "Watch TV" which switches to Video 3 (S-Video) and a button called "Watch HD" which switches to Video 7 (HDMI->DVI).
In the short term, be careful about switching the resolution to 480p just to fill the screen with SD content - it makes your HD content 480p also and even on a 32" TV you'll definitely see the difference. An HDTV with an SD (even 480p) signal is a terrible, sad, sight

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Keep your eyes on this forum for talk about Native Passthrough It may be more months coming, but, maybe, someday, it will...