When designing artificial intelligence (AI) in politicised contexts, such as the public sector, optimistic promises of what AI can achieve often shape decisions around which problems AI should address. Different epistemological views carry different understandings of what is considered the problem at hand, and, as we show in this paper, ethnographic perspectives often fail to match the politicised promises of AI. This paper reflects on personal experiences from an interdisciplinary research project that aimed to take a responsible approach to research and design AI for public services in Denmark. Seeking alternatives to the inflexible algorithms [3, 38] often used to automate or augment specific decision-making tasks in these contexts [1, 2, 35], our research project took a flexible approach to research and design and included ethnographic workplace studies to explore whether AI could both leverage the increasing powers of computing and retain the discretion of the user [23]. Following Mesman [33], we present three empirical moments that were particularly challenging for us as ethnographic researchers and influenced our project in important ways regarding the problems for AI to solve. Problematising [6] them, enabled us to surface how 'readiness', emerging from the politicised context of AI in Denmark, had confounded our efforts at interdisciplinary collaboration. Problematisation, then, allowed us to come to a new understanding of the problem at hand and open up a space to collaboratively re-imagine the problems for AI to solve. This paper is in the spirit of serving as a bridge between our initial and revised understanding, pointing to the ongoing discussion in HCI about 'bridging the gap' between ethnography and design. Our contribution is a discussion of how researchers and designers might engage with problematisation at the frontiers of HCI to develop an open-ended approach to collaborative AI design in politicised contexts.