Uncontrolled light causes lens flare. This can be light that's reflected from internal lens surfaces, or that's scattered by imperfections in the glass.

If the flare is badly controlled, it will produce the dramatic lens flare artifacts which you've probably seen. More controlled flare will be diffused over the entire image, reducing contrast but not producing other visible artifacts.

Flare can be controlled in several different ways. A simple way is just to prevent non-image light from hitting the front element in the first place. Avoid putting bright lights (the sun, for example) directly in the frame, and prevent out-of-frame light from shining onto the lens. This is what a lens hood does — or, simply shading with your hand, in a pinch.

If there is a bright light source (the sun, for example again) that you want to have in your photograph, that's not going to help. That's a reason wide angle lenses are more susceptible to flare (and for the same reason, a lens hood can't be as useful, as a deep one would block the actual image).

On almost all modern lenses, special optical coatings are applied to the lens to help control the stray light. These are made of various metallic and mineral compounds which alter the way the lens transmits light, and they're specially chosen to reduce the unwanted scattering of light. More expensive lenses use more expensive coatings, and more expensive optical elements which have less of a problem in the first place. Lenses also have internal baffles designed to reduce bouncing light.

Cheap filters often have cheap coatings, and since they're often more exposed than the front element was, they're more prone to catching stray light. That's why adding a UV filter for lens protection can reduce image quality.

So, to answer your question directly: yes, it's true. Flare is caused by stray light, not by lens materials directly, but cheap lens materials can make it worse and high-quality ones can mitigate it. Even with a cheap lens, you can make things much better simply by using a lens hood or standing in the shade, and keeping the sun out of the frame.