As Theon Greyjoy noted (in the original novelisation) the person he proclaims guilty for killing three of his Iron Islands men could have done it (the protectionless hound doubtless being the clincher), and it so it is his right to exact punishment for it. The truth being somewhat different meant nothing to the self-styled Prince.
(edit: I am ninjaed, below...)
Whoever is punished, such is the word of the authority (at least at the noble level, unless the player-spirit itself is asked a pop-question like the one where someone is to be raised to nobility, or the even more alike Clue(do)-like attempt to determine the 'true' perpetrator of a terminal desanguinisation). There are already bad thoughts about misplaced justice, which can handle grumblings, if dwarven minds are expansive enough to have their own opinions about responsibility for a mandate.
"All I know is that Urist McCarpenter makes beds, so they're the one that didn't make the steel bed [sic], when asked." "I think it was Urist McSmith, he's the highest-skilled metalworker (*cough*other than me and my husband, but we are obviously not to blame*cough*) and the buck stops there! And he plays music badly too!" "I've not seen any steel. Have you seen any steel? Someone's not been supplying my furnace. Now, I don't mean to snitch, but I'm sure I saw some steel musical instrument pieces when I last went to the Depot, waiting to be purchased and brought back here to be melted..." "Actually, I just think the Mayor's an idiot. As I explain in my largely well-reviewed tome 'Urist McBaroness Is An Idiot, And I Would Be A Marginally Better Baroness Than She', currently being copied ten more times, just awaiting more quires."