] In this context it seems that illiterate does not mean that they can't read and write - I'm inclined to think it means they haven't read much and have only basic literacy skills.

I agree with you here, according to Dictionary.com, the word can have many meanings...

il·lit·er·ate adj
1.

a. Unable to read and write.

b. Having little or no formal education.

2.

a. Marked by inferiority to an expected standard of familiarity with language and literature.

b. Violating prescribed standards of speech or writing.

3. Ignorant of the fundamentals of a given art or branch of knowledge: musically illiterate.