The assumption that ordinary people would be willing to do the most peculiar things to project themselves into the public eye because of an obsession with fame is a DISTURBING idea on modern society. I believe the sentence written like that would sound more natural. But you did a great job! If you need tips on how to improve your english feel welcome to contact me, okay?

'Disturbing' works for me here. It means 'worrying'.

The sentence as a whole is natural, perhaps lacking in pronunciation, but natural. ( I read it as "This story, that ordinary people are willing to do the most peculiar things to project themselves into the public eye, is a disturbing comment on modern societies obsession with fame") see also society-societies. Disturbing works fine in this context, and refers to a feeling of upset/concern/worry/trouble. So in this title it is saying the want of fame is a worrying (or insert other synonym) thing in society due to it's interruption of normality. Hope this helps.