This supervisor sounds like she has some insecurity issues that your good grounding in company functioning has tapped into. And reporting to someone who is less knowledgeable or not as smart as you can be challenging.

That said, for better or worse she is your supervisor and unless you really do want to look for a new job, the best way to get out from under this cloud over your head is to treat this woman with respect and make peace with her. In corporate terms, this is called 'managing your manager'. Doesn't mean you have to like her but if you don't, she doesn't have to know it. she wants to believe that you believe in her.

Call a truce of sorts, soften your attitude, make an amend if you need to for the error you made and maybe the whole thing will blow over. What do you have to lose? After all, you are the one who is suffering.