Yep. Red iguanas are real. It is because of many generations of wild breeding, no humans involved. They even have some physical differences other than the color. If you breed two red iguanas, you will only get red iguanas. If you breed two green iguanas, you will only get green iguanas. If you breed a red with a green, you get brown iguanas, pretty much. The red iguana and green iguana both possess different colors that a co-dominate. They can't cancel each other out, so they merge. Red iguanas are a relevent "breed" of iguana, because they breed true to color. It is true that male iguanas can turn orange-ish due to hormones, but that is completely different. Red iguanas are born red. !!
My red iguana, Salvador, has a very blue/green head recently. It is a sign that they are healthy and happy! Red igs evolved from green igs, so they still possess some green coloring (as you know.. they've got cute green bellies) and their head will be greenish if they are healthy.