O shields the H in OH from splitting. This is because it has a high electron density, and nuclear charge of H in OH cannot penetrate this electron density, thus it does not resonate with other nearby H environments.
Also, it is not true that splitting only occurs with other nucleus 3 bonds away. There are J4 splitting in substituted arenes, and J2 splitting in phosphorus-substituted hydrocarbons and metallic complexes. None of these should mean anything to you right now, but the point is don't make up rules and reasons just because, there are lots of physical principles behind chemistry.

[e.g. the n+1 rule is based on combinatorics (specifically pascal's triangle) in probability, multiplicity often simplifies to n+1 because difference in splitting frequency is tiny, and more often than not addition of ordinates give almost the exact same curve as n+1 would predict]