Nero's playing the fiddle while Rome burned is much in the same vein as Marie Antoinette's advise to hungry Parisians to eat cake,two historic incidents in all probability never were
While Nero,like many of his predecessor,was bit of a megalomaniac,he was also power hungry enough to understand the consequence of earning the wrath of the Romans by destroying the city.Even if he indeed set fire to a part of the city,it was not within this means to keep it burning for six days.
Most of his demonizing happens in the later christian writings,who were severely prosecuted by Nero,esp after the great fire.this continued until recent times,read the polish classic Quo vadis by Sienkiewicz.
Nero was not half a megalomaniac and psychopath as Caligula was.