I'd rather depend on the dictionary definition which is more subtle and less judgmental, but I'm aware that it's become a rather loaded term recently. (A special right, advantage, or immunity granted or available only to a particular person or group.)
> Is a kid who studies and gets all A's in class privileged with getting the reward for all A's?
Overwhelmingly the answer is yes. Children who come from a privileged background tend to make better grades as a rule, and the privilege continues from there. There is no need to get defensive about it or guilt-ridden, either, if you're one of the people in that position. (what, I'm supposed to perform badly so others can catch up?) It is just useful to recognize what is happening.
If nothing else this kind of awareness prevents people from having to ask questions like "Do I just live in that much of a bubble?" Well, yes.
> Earning a scholarship anyone can earn? Not privilege.
It wouldn't be a scholarship if anyone could earn it. No organization that awards scholarships awards them to all applicants performing above a certain objective threshold, as far as I know. It's a contest with winners, and the winners enjoy a certain privilege. There's nothing inherently wrong with that.
(although it might be a big-picture problem if there aren't enough scholarships to go around, if increased credentialism requires too many people to win that particular lottery, etc. etc.)