Did you look up what naturally aggressive means? Bullying is evil...people have killed themselves over bullying so I don't get your comparison.
Ock responded the way anyone would with his life situations. He wasn't naturally aggressive or evil before the accident or he would have walked around punching people for looking at him. Anyone who responds with aggression in every situation either has a problem or they are evil. Ock had weapons before his accident that he didn't use.
Do you disagree that the accident is what made him evil? Do you really think Ock was a bad person before his accident? Just answer those two questions.
*sigh* Before we continue, please note that "naturally aggressive" as I used it refers only to his attitude prior to being fused to the arms. It does not refer to being "born aggressive."
As for bullying being "evil," I suppose that's entirely up to the kind of bullying and to personal definitions of evil. It should also be noted that people with suicidal tendencies don't need to be bullied to commit suicide or to consider suicide. Any number of stimuli may set them off. So those stimuli should also be considered "evil" if that's how you determine morality. If you don't get my comparison then that's really just too bad. Because it's the same sort of AGGRESSIVE behavior Otto displayed prior to becoming Doctor Octopus. If that's your definition of evil, then I suppose you should consider him evil prior to the accident. But I don't, so I contend that he's just being aggressive.
Otto absolutely was aggressive. He didn't have to punch anyone to demonstrate it either. There are other ways to release your aggression and he did just that by creating a hostile work environment, pushing an intern/coworker, and demeaning his colleagues (you're really going to tell me that WASN'T being aggressive?). An aggressive dog does not necessarily bite out of aggression, but may also growl, bark, or bare its teeth. As for having weapons at your disposal, considering aggression does not necessitate the use of weapons, Otto didn't have to use the arms before his accident.
Per your questions: Yes, I do think the accident is what pushed him over the edge to life as a villain. And no, I don't think Otto was necessarily a bad person prior to becoming a villain. I think he was just an aggressive *****e bag. Which is the opinion I have of most aggressive people I know of.
EDIT: Let's go with another aggressive Spider-man character. Flash Thompson. Regardless of the motivation and life events that led to their behavior, both were aggressive. Neither was evil. They were similar in personality (though, perhaps not in social standing and intelligence) and both acted out of aggression.