Yes. That does happen, although I think people trust the PA to supply them with material that can be used without making any further checks. We do sometimes receive telephone calls from picture desks who will ask about the specific circumstances in which a picture may have been taken.
For example, it might be a celebrity who has been photographed accompanied by their children. Before we put that picture out, we would ask those questions about the circumstances: was the celebrity content for their children to be photographed? How could we be sure about that? It might be someone walking through an airport accompanied by their children. We would then have to take a decision whether we had the consent or not, and then if we thought that we didn't, what we would actually do with the picture. It might well be that in any case we would pixelate the face of the children or we might edit the picture so the children aren't included in it.