Institutions of higher education (HEIs) in English-speaking countries have been engaged in internationalization for decades. Among the many factors driving their internationalization are commitments to increasing and celebrating diversity as well as a desire to foster cross-cultural cooperation. Nonetheless, the linguistic diversity of their multi-national student body and faculty poses challenges for HEIs, including the decades-old controversy surrounding international teaching assistants (ITAs) in the United States. Despite their commitments to respecting diversity, HEIs have generally adopted a deficit approach to ITAs' language, framing it as "flawed" and attributing communication problems to those "flaws". I argue that, despite its more nuanced understanding of the issue, applied linguistics has adopted an implicit politics complicit with this dominant framing which leads researchers to ignore the student's role in ITA-student communication. In response, I propose an alternative approach grounded in critical sociolinguistics. Working from this perspective, I examine students' discourse about their international instructors, arguing that their statements suggest contrasting orientations to communication across linguistic difference. Some students seek to cooperate with their international instructors, while others prefer to avoid them. I examine their justifications for these orientations in detail and discuss implications for higher education policy.