Rawan Salem Hussein challenged Governor Sadiq Madlool al-Sultani to an on-air debate on his contributions to "the cultural situation in Babil", and said she would prove that he had "set Babil province back 50 years".
Iraq deploying thousands of troops to retake Mosul
Hussein's father Salem said the fire at the family's home in Hilla, south of Baghdad, occurred not long after the clip was broadcast on Al-Baghdadiya TV.
A police captain said a malfunctioning heater caused the fire, but Salem said that it had been turned off, and suggested that arson was the cause.
The incident "raises a number of questions, especially the question of its timing", he said.
"Why, six hours after the broadcast of the video clip in which Rawan spoke about the governor, was the house burned?"
Salem said he and Rawan were at a protest in Baghdad at the time of the fire.
Rawan was part of an Iraqi delegation to an international cultural festival in France and is an activist for children's and orphans' rights.
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