Generative AI (GenAI) is rapidly entering K-12 classrooms, offering teachers new ways for teaching practices. Yet GenAI models are often trained on culturally uneven datasets, embedding a "default culture" that often misaligns with local classrooms. To understand how teachers navigate this gap, we defined the new concept Cultural Distance (the gap between GenAI's default cultural repertoire and the situated demands of teaching practice) and conducted in-depth interviews with 30 K-12 teachers, 10 each from South Africa, Taiwan, and the United States, who had integrated AI into their teaching practice. These teachers' experiences informed the development of our three-level cultural distance framework. This work contributes the concept and framework of cultural distance, six illustrative instances spanning in low, mid, high distance levels with teachers' experiences and strategies for addressing them. Empirically, we offer implications to help AI designers, policymakers, and educators create more equitable and culturally responsive GenAI tools for education.