Yes, scarlet red hair can be natural.
Red hair, in its various shades, is indeed a naturally occurring hair color. While "scarlet" might imply a very bright and vivid red, natural red hair encompasses a spectrum of shades from deep burgundy and auburn to lighter strawberry blondes. The specific shade of red hair is determined by genetics.
The most significant factor in natural red hair is a mutation in the MC1R gene. This gene provides instructions for making a protein called the melanocortin 1 receptor. This receptor is involved in producing melanin, the pigment that determines hair, skin, and eye color. When the MC1R gene has certain mutations, it results in less production of eumelanin (dark pigment) and more pheomelanin (red pigment).
Therefore, while true "scarlet" may be rarer than other shades of red, the underlying genetic mechanisms that produce red hair in general can certainly result in naturally vibrant red shades that could be described as scarlet. The intensity can also be influenced by other genes and environmental factors.