You have to be skeptical of lurid tales from Roman history in secondary (or in this case, most likely third or fourth hand) sources, quite often they come from as few as one writer of the time. In the case of Nero, there are three sources: Tacitus, Suetonius and Cassius Dio. The first two lived at or close to enough to the time of Nero to have been able to talk to people who were there, while Cassius Dio is writing more than a hundred years later and is generally considered the least reliable of the three. they all tell somewhat consistent stories of Nero; this was a mercurial, murderous and sadistic emperor.

I took at look at all three, and while there's plenty of evidence for Nero's love of murder, of theatre, of acting himself, of staging spectacles of violence, I couldn't find your specific anecdote. Here's a sampling of what I do find with respect to Nero and bits of theatrical sadism:

While holding the offices of praetor and consul, he brought Roman knights and matrons on the stage to act a farce.

Sutetonius

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I think the following story from Cassius Dio might be the source of the anecdote you're citing:

In the course of producing a spectacle at one of the theatres he suddenly filled the place with sea water so that fishes and sea monsters swam about in it, and he exhibited a naval battle between men representing Persians and Athenians. After this he immediately drew off the water, dried the ground, and once more exhibited contests between land forces, who fought not only in single combat but also in large groups equally matched.  On a later occasion some judicial contests were held, and even these brought exile or death to many.

Cassius Dio

Given that "The 4AM Breakthrough" isn't a Roman history of any kind, I'd be skeptical of the precision of the anecdote. Cassius Dio is saying something _a bit_ like what you're reporting, but as you can see, its just one sentence. I imagine your source himself read or heard some other second or third hand source that was parsing the Dio story, and along the way account got injected with some invented detail. Dio isn't the most reliable of historians, but he does seem to be saying something quite similar to what you're reporting from Brian Kitely.

There's a good short note on the subject Nero the Artist-Criminal which nicely sums up what these sources tell us of Nero's theatrical sadism, but keep in mind the skepticism we have about Dio-- he is a classical source, true, but well after the fact -- and while contemporary historians Tacitus and Suetonius give us plenty of reasons to dislike Nero, one suspects that Dio writing later has exaggerations, nonetheless they are exaggerations that stuck to Nero's historical legacy for later readers.

According to Cassius Dio, Nero was accustomed to call Priam marvelously fortunate for having lived to see the destruction of Troy. In this last anecdote Nero shows a desire to suffer the woes of Priam; he identifies himself with Priam, and desires to see the destruction of Rome ( that is, his Troy). Thus we have the picture of him setting fire to Rome in order that he might fiddle while it burned, in order that he might compare, as Tacitus says, "present misfortunes with those of the past."

What we are told of Nero's character is perfectly consistent with this picture. He was a poet, an actor, and a sadist

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