however, I think the school mark "B" is punned at. Could an expert please confirm or deny?

as a writer of humorous song (retired):
IMNSHO all meanings count, and were probably accepted at the time of writing.

Some will hear one meaning and laugh, some will see the other meaning and laugh and some will see both and nod as they laugh.

FWIW Sid Kipper's manager (;-) is a Uni Graduate, Post Grad too.