Real answer: privilege is attained from an intersection of many factors. How many times have you heard someone say "Sure, I'm a white man, but I grew up on a rural farm to poor parents. Where's my privilege?" And in a way, they are correct - socioeconomic privilege is a real thing, and if you're poor the deck is stacked against you.
But put Tim, the poor white farmer, and John, a rich black man, behind the wheel of a BMW. Which one belongs there? Which one gets stopped by the police? Hand Tim an airplane ticket to fly to NYC, and hand one to Hamza, and see who gets the extra TSA pat-down.
In your case, are you an immigrant or on a student visa? Either way that's a disadvantage for sure. Are you as privileged as Biff Kennedy, who had a Nantucket yacht club membership at age two and graduated Groton as an all-star lacrosse player? Nope. But when you and Biff go in for an interview, management is gonna look more like you two than John or Hamza. (Of course, Biff's father already arranged for him to get the job. And if he hadn't, the connections he made from his Skull and Bones days would be more than enough. But that's just Biff's privilege!)
The concept is only flawed under the most cursory of understanding and analysis.
I find that many counter-arguments to privilege will try to dial back the level of analysis to make privilege seem ridiculous.
If you're a white male who is honest with himself, you'll understand that being a white male carries with it a set of privileges.
Just consider: a white child is significantly more likely to go to a school with experienced teachers than a black child, more likely to take honors classes in high school, more likely to get into a good university, and when they graduate, are more likely to get job offers based on nothing more than their white male name[1].
Let's not fool ourselves: humans are not the coldly rational actors we like to think. Ignore the fact that I've already got a leg up on networking because my (white male) peers work the jobs I want to work. When it's time for me to go in for an interview for a software engineering position the odds are overwhelmingly high that every person who interviews me, from the team interview up to senior management, will look a lot like me. That goes a long way in me getting the job - our monkey brains are pretty well wired to look at someone that looks like ourself and think "yeah, he's a competent, trustworthy individual!"
So yeah, I don't think anyone's actually hired in the cold cost/benefit analysis you talk about. There's lots of chances for significant bias to creep in. In reality, if people were hired solely based on the criteria you talk about, and race/gender/... were not considered, I bet we'd see more diverse workforces than we have now.
If someone can figure out how to set up a blinded interview that would be interesting.
[1] http://www.nber.org/papers/w9873.pdf