Is the testimony mentioned in American documents considered false, and what are its implications, and is expiation obligatory for the witness?

Your testimony denying the existence of a fight is a lie and false witness, because testimony is only permissible based on what the witness knows. You could have used allusions instead of lying. You are required to repent for what you did, and there is no expiation due from you. However, if you knew that undue harm would befall the assailant if the American police learned the truth of what happened, and it was not possible to use allusions, and you found no way to avert the harm except by lying, then there is no blame upon you at that time for saving him. Indeed, some scholars have explicitly stated the obligation of lying to save a Muslim or his property.