A patient says that a voice sometimes speaks his thoughts aloud, just after he has thought them, as though echoing them back to him — but he does not believe anyone else can access his thoughts directly, and no one else is mentioned as being aware of his thinking. Before revealing the answer: is this thought broadcasting?

No, this is more consistent with an auditory hallucination of thoughts spoken aloud (thought echo) than with thought broadcasting. Thought broadcasting is specifically the conviction that other people gain access to one's private thoughts; here, the disturbance is a hallucinatory experience of hearing his own thoughts echoed back to him, with no belief that anyone else is aware of his thinking. The surface theme — thoughts becoming audible in some sense — can look similar, but broadcasting requires the belief that others share or perceive the thoughts, which is absent here.