Rapid advances in singing voice synthesis have increased unauthorized imitation risks, creating an urgent need for better Singing Voice Deepfake (SingFake) Detection, also known as SVDD. Unlike speech, singing contains complex pitch, wide dynamic range, and timbral variations. Conventional 16 kHz-sampled detectors prove inadequate, as they discard vital high-frequency information. This study presents the first systematic analysis of high-resolution (44.1 kHz sampling rate) audio for SVDD. We propose a joint fullband-subband modeling framework: the fullband captures global context, while subband-specific experts isolate fine-grained synthesis artifacts unevenly distributed across the spectrum. Experiments on the WildSVDD dataset demonstrate that high-frequency subbands provide essential complementary cues. Our framework significantly outperforms 16 kHz-sampled models, proving that high-resolution audio and strategic subband integration are critical for robust in-the-wild detection.