One of the questions that I find more interesting than the one you are asking (which is "Should an illustrator have the skill to depict something from another culture and/or race?) is to look at what is currently available on the market and are we really being "overly PC" as you are suggesting?
For example, If I walked into a children's book section of a library, and was blindfolded and asked to randomly pull books from the shelf, how many of those books would contain an african-american character? I would bet that if truly asked to do this, you would pull down hundreds of books before you happen to select one with an african-american character. Or, maybe you wouldn't even be able to randomly select one with an african american child as the lead.
So a better question than the one you are asking is "If a professional illustrator can draw any race or culture out there, why are 99% of the books on the shelf only showing Caucasian kids? Why is there not more diversity to choose from? What should non white kids look at that shows them a version of themselves? These are much more interesting questions in my opinion.
That's a very interesting question. If 99% of the books in your area are of white people, what are the demographics of your area? Is it the books don't reflect the demographics or that the books that sell and are stocked don't reflect the demographics? Bookstores will stock what sells and makes them money. But you posed an interesting question and I will stop at the book store in my town and go through a random stack and report what I find.