Because Blackfire hasn't committed any crimes in the Solar System, on Earth, or in the United States.
And since she is in the Solar System, on Earth, in the United States that's the only thing that matters unless the Aliens in question have an extradition treaty with the US.
Furthermore if the crime was legitimate, the planet in question could have contacted the Green Lanterns and requested they apprehend Blackfire.
Yet they didn't do that, which throws doubt on just how accurate their claim of Blackfire as a criminal is.