Not quite. A banding Hero can now attack if played into battle directly from hand even if HHI is active. If the Hero has a CBP or CBN band ability (i.e. Daniel promo) then the Hero can band. However, the Hero is ignored for the duration of the battle unless HHI is negated during the course of the battle. If the Hero cannot/does not band, then the opponent would not need to present a blocker since an ignored character cannot win a battle to rescue a soul.
I feel like there was one other aspect I'm forgetting, but I'm not sure...