Well, in support of a colleague, yes there is theoretical risk involved here.
Firstly, it's not advisable because if an airtight plastic container is exposed to sunlight and the air in the container is at the right humidity, condensation will form on the inside walls of the container, fall to the base and cause damage to the book.
Secondly, in the case of PVC and similar polymers, a complex dechlorination reaction may occur upon long-term exposure to sunlight leading to the emission of hydrogen chloride gas from the plastic. Hydrogen chloride gas when dissolved in water forms hydrochloric acid, but for the purposes we are discussing here, the gas can be regarded as just as corrosive as the acid. These PVC degradation reactions have been known for many years thanks to the work of Ivan and other polymer chemists.
I think it's very likely that the professor had one of these in mind when he was talking to your daughter.
As wildwood points out, ventilation is vital for long-term book storage. We've got irreplaceable books in our university libraries and they all seem to be stored in ventilated secure cabinets or on open shelving. I know the British Library and The Library of Congress use the same system, so if it's good enough for them��