According to the CIA World Factbook the literacy rate for people over 15 in the US is 99%.
The claim may relate to "functional illiteracy," which seems to be a more nebulous concept:
> A definition of literacy and/or functional literacy acceptable to all industrialized countries neither exists nor is it desirable (whatever inconvenience this may mean for international comparison purposes) since literacy is a complex, interdisciplinary and relativistic skill, open-ended in terms of an individual's lifetime and aspirations as well as in terms of possible adaptations to changing times and environments, which should take into account as many factors as possible directly concerning the interests of the people who matter.
\-- FUNCTIONAL ILLITERACY IN INDUSTRIALIZED COUNTRIES: AN ANALYTICAL BIBLIOGRAPHY Ursula Giere