The statement is - True.
The solvent do contains chlorofluorocarbons (CFC) and hydrochlorofluorocarbons (HCFC) which evaporate and enter the atmosphere. Because they are very light, the CFC and HCFC manage to get very high into the atmosphere, reaching the ozone layer in the stratosphere. They are actually the two substances that are the most damaging to ozone layer, as once they get in touch with it, they break down its structure, thus creating the ozone holes.
The ozone is crucial for the survival of the living organisms on the Earth as it is the layer that manages to stop most of the ultraviolet rays form the Sun to reach the surface. Because of that, these two substances have to be replaced quickly as the ozone layer is becoming more and more damaged, and that can eventually lead to a tragedy.