Natural to me is no chemical straightening process or chemically altered hair, including BKT. I just started heat training my hair (because I couldn't get a comb through the crown, wet or dry), but I'm not fully natural yet, just transitioning. And, I do color my hair, and will continue to do so, but I use an "all natural" hair color, one without peroxide, ammonia, etc. That is what natural hair is to me...not chemically straightened. Heat straightened hair can revert to it's natural state if not heat damaged, whereas chemical straightening is a permanent process, where the bonds of the hair are broken, which results in straightening of the hair. I don't get too wrapped up in the word, as I'm just glad to be away from chemicals in the form of relaxers. That gives no concession or prejudice to whatever type of "relaxer" other people use or consider, whether that is heat, texturizers, thio, BKT, etc. Mine is lye. So, I gave up lye, and therefore, I'm going "natural."
ETA: And I disagree that heat trained natural hair is simply damaged natural hair. That is very incorrect. Just because the texture is softened doesn't mean it is damaged, so please study the chemistry and trichology to understand the many ways texture can change. In that case, my taking vitamins (some which soften my NG) results in damaged hair. Not so. There are natural products from the earth, like henna and cassia, which have been known to soften the hair. Heat trained hair is not simply damaged natural hair.