classical mechanics - Is Wikipedia's definition of angular velocity incorrect?

According to Wikipedia, the general formula for the angular velocity of a particle in three dimensions is $$\boldsymbol \omega = \frac{\mathbf r \times \mathbf v}{\left |\mathbf r\right|^2}.$$

But if this were true in general, wouldn't it follow that the angular momentum, $$L = \mathbf r \times (m\mathbf v),$$ is always parallel to $\boldsymbol \omega$?

Or is it simply that we can use different reference points to measure $\mathbf r$ in each formula (as appropriate), and thus we end up obliged to have tensors in our equations?