Through a series of interviews with Boston City employees, we investigate the phenomenon of "grassroots experimentation," where municipal employees independently experiment with AI tools outside of formal procurement channels. This practice of informal, "under the radar" tech adoption is motivated by the inability of procurement guidance to keep pace with the recent proliferation in accessible, low cost AI tools. Our first case study reveals how this self-directed exploration influences AI integration in the highly sensitive application of municipal public services. In three subsequent case studies, we highlight the ethical and security concerns of experimental AI usage at the municipal level. Our final case studies identify strong team leadership and a supportive tech culture - one that recognizes and respects the grassroots experimentation phenomena - as crucial factors in mitigating the risks posed by informal adoption. These insights may be useful for future policy innovation that empowers employees to adopt AI tools to improve municipal service provision in a safe and appropriate manner.