Concerning this Indian police officer who was hesitant to call paying money for a pilot's license a bribe, Indian laws and Indian culture are at play here. If you pay money directly to the person who issues a license it is a bribe, if it is paid to a third party such as a cousin, brother or sister then it is not termed a bribe. That distinction, which is absurd to us, is critical in their culture and virtually their entire economy.
In the example of an engineering student writing only his name and cell phone number on an exam paper, the money would not be paid directly to the exam-grader but instead to a relative of the exam-grader. Then the exam-grader fills out a perfect score paper. Paying the exam-grader directly would be considered a bribe.