Large language models (LLMs) are rapidly being adopted for tasks like drafting emails, summarizing meetings, and answering health questions. In these settings, users may need to share private information (e.g., contact details, health records). To evaluate LLMs' ability to identify and redact such information, prior work introduced real-life, scenario-based benchmarks (e.g., ConfAIde, PrivacyLens) and found that LLMs can leak private information in complex scenarios. However, these evaluations relied on proxy LLMs to judge the helpfulness and privacy-preservation quality of LLM responses, rather than directly measuring users' perceptions. To understand how users perceive the helpfulness and privacy-preservation quality of LLM responses to privacy-sensitive scenarios, we conducted a user study ($n=94$) using 90 PrivacyLens scenarios. We found that users had low agreement with each other when evaluating identical LLM responses. In contrast, five proxy LLMs reached high agreement, yet each proxy LLM had low correlation with users' evaluations. These results indicate that proxy LLMs cannot accurately estimate users' wide range of perceptions of utility and privacy in privacy-sensitive scenarios. We discuss the need for more user-centered studies to measure LLMs' ability to help users while preserving privacy, and for improving alignment between LLMs and users in estimating perceived privacy and utility.