And you can't play Frenzy and have it Sweep twice either, because Frenzy gives you an extra attack action, but Sweep (despite counting as an attack action) is an "arrow" action. But Frenzied Giant could Sweep and attack a character of course.
Well, yes you can. With a Frenzy you give the monster an extra 'attack' action. Remember that the "arrow" does not give any restrictions to an ability (or in this case, attack). It does not require you to exhaust the card (it isn't a magic the gathering 'tap' sign) it merely means you have to use one "action" to perform this. And in this case that action has to be an "attack" action.
We had a debate about this aswell, where one stated that this wasn't an "attack" action per se, but that is was an "action" that happened to let you perform an attack, so it could be used for both actions (like the "howl" ability from the barghest for example). But we desided that it couldnt and if anyone tried it otherwise we would see this as a social problem and pointed them to the d*ck-punching-rule.