Large Language Models (LLMs) are increasingly being used for automated evaluations and explaining them. However, concerns about explanation quality, consistency, and hallucinations remain open research challenges, particularly in high-stakes contexts like privacy and security, where user trust and decision-making are at stake. In this paper, we investigate these issues in the context of PRISMe, an interactive privacy policy assessment tool that leverages LLMs to evaluate and explain website privacy policies. Based on a prior user study with 22 participants, we identify key concerns regarding LLM judgment transparency, consistency, and faithfulness, as well as variations in user preferences for explanation detail and engagement. We discuss potential strategies to mitigate these concerns, including structured evaluation criteria, uncertainty estimation, and retrieval-augmented generation (RAG). We identify a need for adaptive explanation strategies tailored to different user profiles for LLM-as-a-judge. Our goal is to showcase the application area of usable privacy and security to be promising for Human-Centered Explainable AI (HCXAI) to make an impact.