This paper explores how three Science, Technology, Engineering and Mathematics (STEM) lecturers working in English-medium instruction (EMI) grapple with the prospect of self-positioning as English-language-teachers (ELTs), drawing on interviews in which they explicitly deny acting in this way. It begins with essential background, first discussing key concepts such as EMI, internationalization, Englishization in higher education and 'CLIL-ised EMI', the latter understood as what happens when EMI is reframed as sharing key characteristic with Content and Language Integrated Learning (CLIL) -- language teaching. The paper then outlines the main focus -- the notion that STEM specialist EMI lecturers might, on occasion, act as ELTs -- examining selected findings from previous research exploring this topic. This discussion is followed by further background information about the context and the methodological framework adopted here, a revised version of Positioning Theory. These preliminaries aside, the paper presents a series of excerpts from interviews with informants, which then serve to construct a narrative about EMI lecturers as ELTs. In the face of informants' resistance to this identity, the paper ends with some thoughts on what has been learned, both in this context and further afield.