According to Proof Wiki, if a triangle is not equilateral, then its orthocenter and circumcenter must be distinct. The exact quote is
Let △ABC be a triangle.
Let O be the circumcenter of △ABC.
Let G be the centroid of △ABC.
Let H be the orthocenter of △ABC.Then O, G and H are the same points if and only if △ABC is equilateral.
If $\triangle ABC$ is not equilateral, then $O, G$ and $H$ are all distinct.
Well, it looks like I've found a counterexample: $$A=(0,0),\quad B=\left(1-\frac{\sqrt 3}{2},\frac12\right),\quad C=\left(1-\frac{\sqrt 3}{2},-\frac12\right)$$
and the orthocenter and circumcenter both coincide at $(1,0)$, right?
So is my counterexample valid, or did I screw something up?