In fact is generally used when you are contradicting the previous statement with facts. For example:
- When a federal court finds a federal statute to be in violation of the Constitution, as Judge Phillips did in the LCR case, we often speak of the Court "striking down" that federal statute, as if the court's order removes it from the books altogether. That is not, in fact, what happens. Federal courts don't have the power either to enact or to repeal federal statutes. What they have the power to do is declare federal statutes unconstitutional and issue orders prohibiting their enforcement. (Huffington Post, October 24, 2010)
- Mr. Cuomo, the state attorney general, sought to promote an image as someone who can reduce the size of government. He said he would leave the state attorney general’s office smaller than he found it. Indeed, during his tenure, the office has reduced spending by 8 percent and reduced staffing by a similar percentage. (New York Times, October 18, 2010)