No.
Placement tests are generally not valid ways of determining IQ. It just shows how ignorant the person is of the content of the test.
I think the idea our forefathers had was that if the person had enough experience and age then the wisdom would follow.
As far as your example goes, she has kind of put her foot in her mouth a few more times than most, but I am sure everyone says things that are totally incorrect. Does that mean they are stupid?