Large language models (LLMs) are commonly evaluated for political bias based on their responses to fixed questionnaires, which typically place frontier models on the political left. A parallel literature shows that LLMs are sycophantic: they adapt their answers to the views, identities, and expectations of the user. We show that these findings are linked: standard political-bias audits partly capture sycophantic accommodation to the inferred auditor. We employ a factorial experiment across three major audit instruments--the Political Compass Test, the Pew Political Typology, and 1,540 partisan-benchmarked Pew American Trends Panel items--administered to six frontier LLMs while varying only the asker's stated identity (N = 30,990 responses). At baseline, all six models lean left. When the asker identifies as a conservative Republican, responses shift sharply: the share of items closer to Democrats falls by 28-62 percentage points, and all six models move right of center. A mirror-image progressive-Democrat cue produces little change; rightward accommodation is 8.0$\times$ larger than leftward. When asked who the default asker is, models identify an auditor, researcher, or academic; when asked what answer that asker expects, they select the Democrat-coded option 75% of the time, nearly the rate under an explicit progressive cue. These patterns are inconsistent with a purely fixed model ideology and indicate that single-prompt audits capture an interaction between model and inferred interlocutor. Political bias in LLMs is therefore not a fixed point on an ideological scale but a response profile that must be mapped across realistic interlocutors.