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I can understand how one could score lower on the SAT than his/her IQ allows, but I do not see how the opposite could occur if the SAT accurately measures IQ.
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"Measure" is not the most fitting word for any mental test. The long story about why you should prefer the industry-standard word "estimate" can be found in
Amazon.com: Measurement in Psychology: A Critical History of a Methodological Concept (Ideas in Context): Joel Michell: Books
Any mental test has error in estimation. There are no exceptions. Each day's test score is a snapshot based on that day's sample of learned behavior. The person who scores highest of all people on earth on some brand of IQ test might not be the person who scores the highest on the SAT--and the other way around.