The author presents it as though it were based on truth - it may be that it was based on a real person, but the full story was a creative work. The book, the musical, the movies, all had different variations but similar basics.
In the movie he is portrayed as someone who suffered severe trauma and abuse in his childhood. If we consider the times (1870 to start) and the culture, it would make sense that someone with a distortion would be shunned by society. Often people were superstitious then and believed that disorders now known to be Medical and/or Mental health problems were demonic. It may be that there was a man living in the basement of the Opera house, maybe homeless and aimless, simply seeking shelter. Someone like that could have inspired the writer.
If we think in terms of the presentation in the most recent movie (2004), with a past like that one would expect him to also be mentally disturbed (In lyrics at one point, Christine sings "this haunted face holds no horror for me now, it's in your soul that the true distortion lies)." The Soul was thought about differently in those days and characteristics such as these were often attributed to it.
I don't suppose we'll ever really know.