How can the government investigate itself?
It can, of course. But the results are atrocious when it comes to presenting the undisputed facts of events.
To investigate the murder of President John Kennedy, the new President, Lyndon Johnson, appointed a commission of seven members to what became known as the Warren Commission. This commission took the place of other groups that sought to call witnesses and examine evidence, such as a grand jury in Texas.
The Warren Report did not deliver the facts of the case. Instead it ignored reliable witnesses and allowed fabricated evidence in its conclusion, which was designed to blame an innocent person for what only agents of the government could have done.
Other government agencies and commissions have failed to arrive at the truth. A group of Los Angeles Police Department officers, including Robert Houghton, wrote Special Unit Senator to give the government's account of the murder of Robert Kennedy. They, too, framed an innocent person in part by distorting the distance and the direction the accused was in relation to Kennedy and ignoring overwhelming evidence of bullets unaccounted for.
Many years after the fact, a Congressional committee considered the "October Surprise" story of Ronald Reagan campaign advisors making a deal with the Iranian leaders to delay the release of United States hostages. The Committee ignored evidence of the Iranians suddenly becoming uninterested in talking to the Jimmy Carter Administration, pilot testimony of flying Reagan's representatives to France and Vice-Presidential candidate George H.W. Bush's hollow alibi in whitewashing the whole story.