From my studies into the background stories of 1 Peter, Nero loved to destroy things...and then rebuild them. Long story short, for whatever reason, Rome was next on his list.
So the front part of the “Nero fiddled while Rome burned” is that Nero set the fire.
Problem was, the Romans weren’t too happy about their city being burned down, and looked to hold someone responsible for it. So Nero needed a scapegoat - and created one in the Christians. Thus was started a horrible period of persecution against the Christians in Rome, which included the invention of the “Roman candle” - dipping a person in pitch (oil), and setting him/her on fire, in order to light Nero’s garden, while he played his fiddle.
So the old saying “Nero fiddled while Rome burned” doesn’t go far enough - to tell that Nero burned it, and meant to burn it. Thankfully Soetoro hasn’t dipped any Tea Partiers in oil and used them to light the White House organic garden...yet...
The historical records are not extensive enough, or unbiased enough, for us to be able to determine whether and to what extent Nero was responsible for the fire or dragged his feet on attempts to put it out.
He certainly did use the Christians as scapegoats, though.