If you don't know anything about how a utility Co integrates their power system, and you know the Sun doesn't shine at night, there you are. A person in her position should have a responsibility to know more, but I'm sure a lot of people who know nothing about electricity beyond how to put a plug in the wall would make the same assumption that solar power will leave them in the dark at night, and so whether it's ignorance or demagoguery on her part it's going to play to that audience.
TBF, the question of where base load power is going to come from in areas with a high % of solar power generation is not a trivial engineering question, but it's not a any kind of show stopper either. There are plenty of candidate solutions, obviously including battery storage. In many areas wind power is more available during the night than during the day depending on local conditions. The market hasn't even begun to shake out what combination of solutions will be practical and they will vary in different areas of the country depending on things like whether there is local nuke, hydro, or clever storage facilities like the Luddington pumped hydro station.