NEW YORK ( TheStreet) -- Scott Thompson served as chief executive officer of Yahoo! ( YHOO) for four months, which is about long enough to have a cup of coffee. That means he left no legacy, right? And that Yahoo! does not need to face the issue of staying the course or shifting gears. Since Thompson's hands did not have time to get work-worn, traders can pretend he was never even there. If only life -- and Yahoo's current plight -- were that simple. But speaking of simple, let's talk media coverage of the issue. If you are not aware, you can be misled. In The New York Post and on CNNMoney, it's as if Thompson had no tenure. They don't mention a single initiative. Many others -- like The Associated Press -- make mention of one act: his firing of 2,000 employees, nearly 15 percent of the workforce. New York Times ( NYT) gets it right, so pay attention. They mention the canning of 2,000, but add that it was in essential areas of operation like advertising and user personalization. Moreover, the Times sheds light on Thompson's support of the Facebook suits over patents, right after integrating the social media site and the flirtations with Google ( GOOG), which raised the ire of Microsoft ( MSFT). Thompson was also looking to pull Yahoo away from its media focus, a huge maneuver because, as the Times points out, the company "drew nearly all of its $5 billion in revenue last year from display and search ads." In the end, Thompson was, in fact, a man of considerable influence, despite his abbreviated stay. The company will change without him, an important dynamic to note -- and one the media all but ignored.