Accha: another thing; you asked what they're trying to hide from public eyes; sure, most of those dark tinted cars are done for style and looks; but Qatar and other similar countries are a private and conservative culture.
Many people, including myself, feel very uncomfortable when people stare into one's car. I know it's the public road but i still feel it's really rude to look into other cars. I never ever look at anyone in their car and yet i always get people staring into my car at lights or wherever.
I'm not talking about a casual bored accidental look and rather am talking about those who endlessly rudely stare and stare. We need to remember that the Arab culture (and muslims in general) values and guards privacy. They had tall walls around their homes in the past and it's still visible in their modern architecture too.
Even in the West, people guard their personal space and it's just not proper to stare at others without reason. I'd have my windows super dark too if it was legal; that's how much it annoys me and others when strangers look into our cars while we're eating or with our families or doing whatever the hell people do in their cars. Hope this helps with that doubt of yours :-)