This paper addresses the problem that large-scale language models (LLMs) require both contextual knowledge and parameter memory, yet these two sources of information can conflict. Previous research has reported a preference for parameter knowledge in situations of conflict, but has focused only on tasks requiring reliance on a given sentence. This study uses a model-independent diagnostic framework that automatically detects mismatches between a model's beliefs and a curated knowledge set and injects controlled conflicts into the task. We investigate how this behavior manifests depending on the amount and type of knowledge required by the task. Using a dataset encompassing two mutually orthogonal dimensions (task knowledge dependence and conflict validity), we evaluate a representative open-source LLM and find that performance degradation due to conflicts is correlated with the task's knowledge dependence. Furthermore, we find that explanatory evidence and simple repetition increase contextual dependence, but are detrimental when parameter knowledge should dominate. This behavior raises concerns about the validity of model-based evaluations and highlights the need to consider knowledge conflicts when deploying LLMs.