I actually agree with you that pre-BftC Jason was really an anti-hero (he did really bad and uncalled for things like beating the crap out of his brother out of jealousy, but he also saved innocent people, killed criminals who targeted children and/or were really evil, and he was less ruthless than the Punisher who is considered THE comic book anti-hero). But, he fought Batman and the Batclan, who are the official heroes of the comics, so officially Jason was supposed to be the villain.