Do people even read the words in this series?
Medaka herself even says that she isn't right but she tries to be right. Unzen himself kept on criticizing her to the very end and even states how she may be wrong at various points. She just follows her own beliefs even if it means rejecting the reality around her. Medaka herself even states that she isn't perfect either and that she is full of contradictions more than once over the course of the series. In terms of her trying to do what she thinks is right, she does what most other shounen main characters do. If you can't be reasoned with she will beat you down if you are a threat to her friends and other people. (Or a threat to herself post-Nabeshima pep talk.) If you aren't in the first category, she will use her abilities to pressure you into what she believes is right which we saw with the kendo club and the members of the swimming club.
Being super human does not mean she is infallible. She is just "an abnormal even among abnormals" like the rest of the people in the 13 party so she seems that way at first glance. Lets not forget that Unzen thinks he is still right too and has a fair share of idol worship among his enforcers like Medaka has among her student council.
If anything, it just seems to be an ability among certain abnormals to garner that level of devotion from others. Of course
Shiranui outright hates said ability which makes it even more interesting in a way.