An Arizona graduate student with advanced colon cancer turned to Twitter when his insurance company stopped covering his medical bills. Surprisingly, the insurance company’s chief executive responded. What ensued was a fiery multiday exchange that not only resulted in full coverage of the student’s medical bills, but cast light on gaps in student health care coverage and the complexities of the country’s private insurance system. Arijit Guha, 31, a New York native who was raised in Ohio, learned he had cancer in February 2011. A doctoral student at Arizona State University, Mr. Guha was insured under an Aetna Student Health plan for which he paid $400 a month.