The sycophancy of language models, or their failure to push back against faulty user input, is now widely studied. However, if LMs do push back, is sycophancy solved? We show that LMs vary in how they present pushback, and thus vary in how effectively they correct user beliefs. We introduce a phrase-level, human-validated response labeling framework to uncover fine-grained insights into how LMs push against and/or affirm false inputs. We develop and apply our framework on model responses in five languages: English, German, Chinese, Hindi, and Yoruba. We find that when models do push back against users' false assertions, they tend to use indirect phrasing and mix in affirmation, with more indirectness in Hindi and Yoruba than in other languages considered. In a large-scale human study (n = 300), we find that the pushback ambiguity we identified may fail to correct and prevent users' factual misconceptions.

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