Well, if she doesn't mention this company on her work record, it's going to show up as a former employer during the background check, which all large corporations do.
Also, if she doesn't put them down, there's going to be a gap in her employment history, that she'll have to explain. If she makes up some story about what she was doing during that time, again, she'll be caught during the background check.
Dirty 12, they didn't lie to you. They said after 90 days you would be "eligible" for rehire. That certainly doesn't say they are under obligation to rehire you.
Being violent and/or verbally abusive is reason for immediate termination. I certainly would never hire or rehire someone who was threatening to other employees.
Why do you think you are deserving of rehire?
It doesn't sound like you are willing to be accountable for your actions. That means in your case not blaming the company for lying and being vindictive, but admitting that you royally screwed up.