Students in Appalachia have a heritage of problem-solving. We explore how computational thinking (CT) relates to and complements this heritage by analyzing 34 local ingenuity stories, and perspectives from 35 community members about the relevance of CT. We found the two problem-solving approaches are meaningfully different, but can be used in concert. Since equating them could contribute to confusion and cultural erasure, researchers and educators bringing CT as a problem solving strategy into rural and other resourceful cultures must clarify what they mean by "CT helps problem solving." In these cultures, CT skills are better introduced as new tools to expand students' problem-solving toolkits, rather than tools that are identical to or better than those traditionally used in their culture.