Filtered Vector Search (FVS) is critical for supporting semantic search and GenAI applications in modern database systems. However, existing research most often evaluates algorithms in specialized libraries, making optimistic assumptions that do not align with enterprise-grade database systems. Our work challenges this premise by demonstrating that in a production-grade database system, commonly made assumptions do not hold, leading to performance characteristics and algorithmic trade-offs that are fundamentally different from those observed in isolated library settings. This paper presents the first in-depth analysis of filter-agnostic FVS algorithms within a production PostgreSQL-compatible system. We systematically evaluate post-filtering and inline-filtering strategies across a wide range of selectivities and correlations. Our central finding is that the optimal algorithm is not dictated by the cost of distance computations alone, but that system-level overheads that come from both distance computations and filter operations (like page accesses and data retrieval) play a significant role. We demonstrate that graph-based approaches (such as NaviX/ACORN) can incur prohibitive numbers of filter checks and system-level overheads, compared with clustering-based indexes such as ScaNN, often canceling out their theoretical benefits in real-world database environments. Ultimately, our findings provide the database community with crucial insights and practical guidelines, demonstrating that the optimal choice for a filter-agnostic FVS algorithm is not absolute, but rather a system-aware decision contingent on the interplay between workload characteristics and the underlying costs of data access in a real-world database architecture.