Heh,
Well you nailed it by sayingImagine 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 importance of the Iraq war"... so Bush isn't showing any signs of apology/regret about the criticism laden against him (for starting/continuing the war) or tries to soften the speech in any way. So pretty much exactly like you said.Well, coming from the word structure it should be "without apologies" or without some formal phrases to soften the speech.