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Heh,

Well you nailed it by saying

Imagine a situations where there might be something to apologize for. For instance Bush and the War in Iraq. We can say "Bush unapologetically spoke about the...

Well, a simpler one "he spoke unapologetically in the interview"

недвусмысленно and бесцеремонно are not bad, but I guess just like the word "challenging" you just don't have a word for...

Ahh...I see. Basically you're seeing it as "decisively"... I guess it's the closest thing. There don't seem to be any proper equivalents to this very special word.

How do you say "unapologetically"? As in

"he unapologetically reaffirmed his religious belief to her"