Yeah, the change of meaning is often very subtle, and people can sometimes disagree on the direction of the change.
Usually though, the device is used to express a kind of understatement. Compare these statements:
He's not bad looking
He's good looking
Which one would you say is stronger? I think most people would say that the affirmative "He's good looking" is stronger than the first version. Another example:
It's not without flaws
It's flawed
If you say "not without flaws", you're usually saying something like "it's good despite its flaws", so that version understates the case compared to the other one.
Again, though: my point was mostly that the meanings are distinct and that language is not mathematics. You can't just replace two minus signs with a positive one and expect the to get the same thing on the other side. Nor should you follow any simple "rule" like that blindly.