What your teacher told the class is true, though it's more complicated than that.
For any flowing fluid there are two types of force. The viscous force is due to the viscosity of the fluid, and that's the obvious force that everyone thinks about. However a fluid has a mass, and therefore when it's moving it has a momentum, and therefore whenever the fluid changes direction the momentum changes and this produces a force. These forces are known as inertial forces.
As a general rule, when viscous forces dominate the flow is laminar, and this tends to happen at high viscosities and low flow rates. When inertial forces dominate the flow is turbulent, and this happens at low viscosities and high flow rates.
We define a parameter called the Reynolds number, which is basically the ratio of the inertial forces to viscous forces. So a high Reynolds number means turbulent flow and a low Reynolds number means laminar flow. The expression for the Reynolds number varies depending on the system, but for example the equation for the Reynolds number of a fluid flowing in a pipe is:
$$ Re = \frac{\rho v D_H}{\mu} $$
where $\rho$ is the density, $v$ is the flow velocity, $D_H$ is the effective pipe area and $\mu$ is the viscosity. So the dependance on viscosity is:
$$ RE \propto \frac{1}{\mu} $$
and as your teacher says, high viscosity means a low Reynolds number and therefore the flow is more likely to be laminar.