The rise of music large language models (LLMs) demands robust methods of evaluating output quality, especially in distinguishing high-quality compositions from "garbage music". Curiously, we observe that the standard cross-entropy loss -- a core training metric -- often decrease when models encounter systematically corrupted music, undermining its validity as a standalone quality indicator. To investigate this paradox, we introduce noise injection experiment, where controlled noise signal of varying lengths are injected into musical contexts. We hypothesize that a model's loss reacting positively to these perturbations, specifically a sharp increase ("Peak" area) for short injection, can serve as a proxy for its ability to discern musical integrity. Experiments with MusicGen models in the audio waveform domain confirm that Music LLMs respond more strongly to local, texture-level disruptions than to global semantic corruption. Beyond exposing this bias, our results highlight a new principle: the shape of the loss curve -- rather than its absolute value -- encodes critical information about the quality of the generated content (i.e., model behavior). We envision this profile-based evaluation as a label-free, model-intrinsic framework for assessing musical quality -- opening the door to more principled training objectives and sharper benchmarks.