For example, a family member who you would address as "sir" (at least in the Southern U.S.), maybe a parent or grandparent, might be taken aback if you addressed them with the formal "usted" in Spanish, because it didn't imply respect, but that you didn't consider the person close. Another example would be prayer, where God is definitely superior to us, but you would address Him with the less formal "tu", because the love He has for us makes that a close and personal relationship. (I'm not even sure that the word "formal" is the right one to use here, as like I say, it's not quite the same as in English.)
You could also have a business conversation where you'd use "usted" without necessarily implying respect, because "tu" sounds out of place for a distant relationship like that. (I.e. using "tu" wouldn't be disrespectful, so much as it would just be weird or akward.)
Am I misunderstanding the usage of the two forms, or could someone enlighten me a bit more on the subject? Is the dynamic similar in other T-V languages, or is it used more to denote social status/tiers?