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In her resignation statement, she said that negative media coverage forced her out.

Penn State University continues to rebuild its image after the Jerry Sandusky scandal, an ordeal that claimed the school presidency of Graham Spanier — considered one of the premier educators in the country — and a number of other high-ranking officials. The scandal and Penn State’s handling of it — including the firing of the school’s seemingly untouchable football coach, Joe Paterno — became perhaps the biggest controversy in America.

Taking all blame

At Rutgers University in New Jersey, President Robert L. Barchi clings to his post despite continuing calls for his removal after a video came to light this year showing the school’s college basketball coach verbally and physically abusing players. The footage was seen by thousands on the Internet, and was played repeatedly on ESPN and on nightly news broadcasts.

Mr. Barchi is facing more fire after hiring athletic director Julie Hermann, who also has been accused of mistreating athletes during her time as volleyball coach at the University of Tennessee.

It’s impossible to say just how much responsibility Mr. Barchi personally bears for what took place at basketball practice, but the coverage of the Rutgers controversy and others like it can create a scenario in which schools’ credibility is put at risk, Mr. Hurley said.

“The public will never know, but how many calls and emails and letters did Rutgers get from prospective, past and current donors saying ‘I’m done’ because of what happened?” he said. “Go down the line, Penn State, any other institution,” and you likely will find similar backlashes.

Mr. Garvey and other presidents realize they ultimately may be held responsible for any campus controversy. But micromanaging what happens at every basketball practice or in every classroom simply isn’t an option.

“You could write a book about the things I don’t know. It’s worrisome,” Mr. Garvey said. “And yet, everybody has limitations.”