The steps listed in the question are not far off, but not quite correct. A more correct list would be:
Indications that a crime has been committed, or is in progress or planned come to the attention of the police. This might be via a complaint, or the report of an informant, or through the police's own observations.
The police decide whether the matter warrants investigation. They are never required to investigate, although credible allegations of serious crime will usually be investigated. The police may consult the office of the prosecutor.
The police seek for and assemble evidence, if possible. They may interview suspects and possible witnesses. This may last anywhere from hours to years. They may seek warrants for searches or wiretaps or arrests.
The police decide whether or not to forward evidence to the prosecutor's office, seeking a charge. They may choose not to do so.
The prosecutor's office reviews evidence submitted by the police, and decides whether to file charges. A prosecutor has wide discretion to proceed with or drop a case. The prosecutor may direct the police to make further investigation if additional evidence is needed or wanted. The decision to file charges will be based on the seriousness of the matter, and on the prosecutor's judgement as to whether a conviction can be obtained, and the available resource of the office. Political factors may come into play.
There may be a grand jury proceeding to review the evidence and produce an indictment. The Grand Jury can hear witnesses. Usually its proceedings and the list of witnesses are tightly controlled by the prosecutor. It has been famously said that any half-way competent prosecutor can get a Grand jury to "indite a ham sandwich". However, the Grand Jury has the power to push inquiry in directions not approved by the prosecutor, although this is quite rarely done in practice. In some states a "preliminary hearing" may be held instead. In either case the question is whether there is probable cause to believe that a crime has been committed, and that the defendant(s) committed it. If the crime is a misdemeanor then the prosecutor can file charges without a Grand Jury or a preliminary hearing.
Charges are filed with the court that has jurisdiction. The defendant(s) may be arrested, or agree to attend court. The defendant(s) will appear to respond to the formal charges, usually with a "Guilty" or "Not Guilty" plea.
The Judge of the court will set the schedule for further proceedings, including a trial if things get that far. The defense may ask the Judge to dismiss the charges, which the Judge may do if they do not appear to be legally well founded.
This process could stop at any stage, and several people have authority to determine if it proceeds or not. The senior police officer(s), involved, the prosecutor, and eventually the judge all can halt the process, at one point or another.
As was mentioned in a comment by Paul Johnson , the supreme court in the case of Brandenburg v. Ohio, 395 U.S. 444 (1969) has significantly limited prosecutions for incitement to situations involving speech that is "directed to inciting or producing imminent lawless action and is likely to incite or produce such action". Otherwise the protections under the First Amendment to the US Federal Constitution protect the speech and prevent any prosecution. Prior to that case the case of Schenck v. United States, 249 U.S. 47 (1919) allowed prosecution for speech that "creates a clear and present danger". The very well-known passage is:
The most stringent protection of free speech would not protect a man in falsely shouting fire in a theatre and causing a panic. ... The question in every case is whether the words used are used in such circumstances and are of such a nature as to create a clear and present danger that they will bring about the substantive evils that Congress has a right to prevent. It is a question of proximity and degree.
Whether prosecution in a given case is allowed under the First Amendment is a question of law for the Judge and perhaps for an appeals court. But I doubt that the reported speech would pass the Brandenburg test or even the earlier "clear and present danger" test. If not, no valid prosecution could be brought.
