I was able to find the following information on the BaByliss brand production site on the Internet:

"BaByliss does not operate its own manufacturing facilities, only sales offices, development centres (Stamford/USA, Hong Kong/China, Liège/Belgium) and logistics sites (Iwuy/France). The appliances are produced by Conair plants (including in Chiuduno/Italy) and contract manufacturers."

Italy does indeed appear to be one of the production locations.