The story of how ‘Nero played the fiddle while Rome burned' originates from a rumor that spread amongst the distraught citizens of Rome following the great fire.

The historian Tacitus writes: "his measures, popular as their character might be, failed of their effect; for the report had spread that, at the very moment when Rome was aflame, he had mounted his private stage, and, typifying the ills of the present by the calamities of the past, had sung the Destruction of Troy."

In his writings, Tacitus presents the claims as rumor and later goes on to state that they are unconfirmed by eyewitness account.

However, another historian writing at around the same time, Suetonius, does present the following account:

"Viewing the conflagration from the tower of Maecenas . . . he (Nero) sang the whole of the Sack of Ilion in his regular stage costume."

Due to the contradictions in both historians claims, we will never know for certain the veracity of the rumors. However considering the differing details in both claims (different types of songs and locations) as well as the negative bias flavian era historians held towards Nero we can infer that Tacitus is most likely correct in his assertion that the rumors are in fact baseless.

Note that both accounts make no mention of instruments, let alone fiddles. But more often than not, singing was accompanied by playing on the Kithara, a common string instrument at the time.

The presence of the Kithara during Nero’s singing is heavily implied from the writings of the historian Dio Cassius a century and a half later:

"Nero ascended to the roof of the palace from which there was the best general view . . . and assuming the kithara-player's garb, sang the Capture of Troy. . . ."

Now you see, the word ‘fiddle’ in past English and even today often refers to the playing of any string instrument, not just the fiddle itself. So Nero’s supposed ‘fiddling’ on the kithara ended up attributed to the instrument itself, despite the fiddle not even being invented during Nero’s time. And so the story of how Nero played the fiddle while Rome burned continues to be in our mindset to this day.

Source:

"The Classical Journal- Nero Fiddled While Rome Burned" - Mary Francis Gyles (1947) (http://penelope.uchicago.edu/Thayer/E/Journals/CJ/42/4/Nero_Fiddled*.html#note84)