With all due respect, "natural light photographer" is often a euphemism for someone who hasn't studied and mastered what flash can do.
I love natural light and always prefer to use what the scene gives me. But I'm not willing to let poor light or a cloudy day limit your photos. I'm not a flash junkie who lights every scene artificially either — much as I admire the creativity of guys like Jason Vinson. As a wedding photographer, my work is about capturing light, and that means having the equipment and knowledge to add and shape it when the setting doesn't give it to me. I show up to every wedding with at least two light stands, four flashes, and an LED light cube.
I always talk through flash with my couples ahead of time. Some couples want a fully documentary feeling and don't want light stands popping off during their reception. I'm mindful about that balance: unobtrusive versus getting the best possible result. You will never find me using flash during a ceremony — maybe during the walkout, never during the vows.
Lately I'm loving direct flash for reception and sunset portraits. For family or wedding party portraits, especially indoors, you might find me running two studio strobes on stands with umbrellas for even, high-end-looking light across everyone's faces.
In short: I'm a student of light. Knowing how and when to use flash, tastefully and intentionally, is part of how I work.