Fran Dreisser character

During the scene where Jack mascerades as the principal to the kid's mom, Fran Dressier, she has got to be not too bright to have immediately fallen for the charade. First, when she says how she just spoke to the real principal on the phone only minutes ago, and then the "replacement principal" Jack steps in such a short time later after the real principal "getting sick"? Anyone somewhat intellegent would know there's no way all that could happen and a replacement principal could step in such a short time later, especially with what the " replacement principal" Jack was telling her. He was telling her about her son like he'd already been working with him for a while telling her "your son's on a role, he's shown lots of improvement, he's the smartest kid I've ever known." And Fran immediately buys into it. And then the way "replacement principal" Jack was describing what happened to the real principal, "he had the runs, the squirts, diarrhea, he had appendicitis". Yeh, putting aside a "principal talking like a 10 year old and Fran not noticing and she didn't know anything about the real Jack and his condition", it's like diarrhea and appendicitis have anything in common, like there's anyway it could've all happened so fast, principal being rushed to hospital, the diagnosis coming back to the school so fast. Fran not only immediately buys absolutely everything "principal Powell" told her, but immediately starts to like him and asks him out. Did anyone else notice how stupid the whole scene was? Even if it was intended on a comic level which didn't work in this film anyway since a plot like this shouldn't have been made into a comedy.