Under the Act, the Federal government can decline to be involved but apparently a person/s can do so.
"The False Claims Act is 31 U.S.C. Sections 3729 through 3733. Qui tam, under the False Claims Act, allows persons and entities with evidence of fraud against federal programs or contracts to sue the wrongdoer on behalf of the United States Government. In Qui tam actions, the government has the right to intervene and join the action. If the government declines, the private plaintiff may proceed on his or her own. Some states have passed similar laws concerning fraud in state government contracts."