Dear Mr. Venkatnarayanan,
Yes - you're absolutely correct, John Williams deliberately used the same notes that Brahms wrote in his Academic Festival Overture. Forgive me if I didn't explain clearly what I was trying to say.
I think what's important here is the spirit in which this quotation should be taken. Usually when we think of plagarism, we think of something dishonest or disreputable. I think what John William did here is commendable instead. He wanted to have fun by paying homage to the same jovial sense of humor Brahms had in borrowing this College song in the first place. Brahms didn't write this tune - it's a folk song that was known in Germany for generations.
Another example of this kind of thing can be found in the last movement of Haydn's Symphony No. 104. His so-called 'London' Symphony. Haydn was adored by the British, and in this piece, he quotes a tune that pays homage to London itself.