There is no such thing as "correct" English.
You be writin' in Ebonics in a college English class an' see what da mofuggin teacha say about it, foo.
Spoken English is not written English. Double negatives always parse as positives when written.
The point remains, though, that going by current most-widely accepted theories of linguistics as an academic subject, there is no such thing as a universal "correct" version of English. Grammars and dictionaries are descriptions of the way people speak, not prescriptions for how they should speak. Identifying one variant of language as correct and another as incorrect is a cultural bias, and not an appropriate thing to do while studying the language in question from an academic perspective. Therefore, to make any definitive statement about English grammar, particularly one as controversial as "double negatives always form a positive", is clearly not the kind of thing you would expect an academic in the field of linguistics to say.
This does not mean, however, that they wouldn't prescribe a particular dialect and set of grammatical rules that they expect their students to use. To require a particular variant of a language in a particular context is a matter of practicality, and is somewhat orthogonal to the study of the language from an academic perspective. (Consider that the students could be studying French and writing their essays in English, for example.)
 All of which kind-of detracts from the joke. Change the MIT professor to a high-school English teacher and it works much better.