Automated fact-checking is a crucial task that supports a responsible information ecosystem. While recent research has progressed from text-only to multimodal fact-checking, a prevailing assumption is that incorporating visual evidence universally improves performance. In this work, we challenge this assumption and show that the indiscriminate use of multimodal evidence can reduce accuracy. To address this challenge, we propose AMuFC, a multimodal fact-checking framework that employs two collaborative vision-language models with distinct roles for the adaptive use of visual evidence: an Analyzer determines whether visual evidence is necessary for claim verification, and a Verifier predicts claim veracity conditioned on both the retrieved evidence and the Analyzer's assessment. Experimental results on three datasets show that incorporating the Analyzer's assessment of visual evidence necessity into the Verifier's prediction yields substantial improvements in verification performance. We will release all code and datasets at https://github.com/ssu-humane/AMuFC.