Per Wiki:
In 1947, he began attending Stockton Wood Road Primary school. He then attended the Joseph Williams Junior School and passed the 11-plus exam in 1953 with three others out of the 90 examinees, thus gaining admission to the Liverpool Institute. In 1954, while taking the bus from his home in the suburb of Speke to the Institute, he met George Harrison, who lived nearby. Passing the exam meant that McCartney and Harrison could go to a Grammar school rather than a secondary modern school, which the majority of pupils attended until they were eligible to work...
“McCartney later took his A-level exams, but passed only one subject—Art”
http://en.wikipedia.org/wiki/Paul_McCartney
it seems his comment is just representative from what we’ve learned about his own schooling