Is it true that viruses cannot be seen with phase-contrast microscopy?
It is true for most viruses. They have a size of roughly 1/100 of bacteria (or smaller), so they are too small to be seen in light microscopy. According to Wikipedia the maximum limit with light microscopy is around 1500x magnification (or making structures, which are at least around 200nm in size visible). 

A lot of viruses are smaller, for example the influenza A virus is around 80-120nm, the HIV virus around 120nm and the rhinovirus which causes the common cold around 30nm. They would only be visible in electon microscopy. The measles virus on the other hand has between 350 and 400nm and should be visible in light microscopy. However, since you are very close to the region where you reach the diffraction limit for visible light, it is usually not used very much.