Could rinsing hair with only water (in shower) strip the hair of its natural oils?

Unlikely.: A small amount will be rinsed away, but water and oil do not mix well. That's why shampoo is required to remove excess oils for many people, though in others the oil is desired. So long as you're not using a soap or detergent, it's unlikely that a significant amount of your scalp's natural oils will be removed with a plain water rinse.