Absolutely correct, John. The lens hood is the culprit here. That's why it's always best to use a hot shoe mounted flash, such as an SB-600 or -700 or -800 or even the expensive -900 models.
Just as an afterthought here, I should mention that if you're going to use the on board pop up flash, be prepared to change your camera batteries often. Pop up flashes are notorious for sucking a lot of juice out of batteries. Hot shoe mounted flashes carry their own batteries. Just something to remember.