Publicly available Generative Artificial Intelligence (GenAI) tools are said to liberate students from the instrumental use of English and empower them to write creative texts to communicate with different communities. This paper reports on an undergraduate language-related service-learning subject in a Hong Kong tertiary institution. In the subject, students co-created digital stories with asylum-seeking children, in written and podcast formats, with the help of GenAI. The qualitative content analysis of semi-structured interviews with the students found that this experience expanded the students' creative potential. Meanwhile, GenAI played a peripheral role in the story creation processes, in that the students exercised agency to use the tools and remained critical of the AI-generated content. This study argues that digital storytelling with GenAI, when used critically, promotes linguistic, digital and cultural awareness among ESL learners, offering them a third space to interact with culturally diverse communities in Hong Kong and giving them genuine ownership of English for creative and communicative purposes.