I didn’t give the prosecutor enough credit, when I pre-guessed that his response would be “out of time”. But he did throw a procedural wrinkle at me: Municipal Court judges can’t grant a writ. From Article 11.05, Texas Code of Criminal Procedure:
Art. 11.05. By Whom Writ May Be Granted.
The Court of Criminal Appeals, the District Courts, the County Courts, or any Judge of said Courts, have power to issue the writ of habeas corpus; and it is their duty, upon proper motion, to grant the writ under the rules prescribed by law.