This is in the context of the various changes in oxidation state the permangananate ion can undergo with the variation of the pH of the medium. Besides the cases of strongly basic and strongly acidic media, the case for neutral media (with reduction to $\ce{MnO2}$) in my notes has a footnote; that this medium is in fact slightly alkaline, due to it being a solution of $\ce{KMnO4}$.
I tried to reason this out. It looks like $$\ce{K+ + MnO4- + H2O -> K+ + OH- + HMnO4}$$ is how it works out.
A quick google search establishes the pKa of HMnO4 to be -2.25. So it makes a pretty good acid in comparison to water.
Thing is, in that case, the product side should have an $\ce{H2O}$ instead of the constituent ions, with the potassium permanganate dissociated. That means the solution's neutral. Which apparently it isn't, going with my notes.
Where did I mess up here?