Machine-generated texts (MGTs) produced by large language models (LLMs) are increasingly prevalent across various applications, while their potential misuse in fake news propagation and phishing has raised serious concerns, highlighting the need for MGT detection. Existing paragraph-level detection methods commonly treat MGTs as entirely machine-like, overlooking the hidden human-like nature of machine-generated texts: even fully machine-generated texts may contain spans that are highly consistent with human writing. To this end, we first reveal the existence of such hidden human-like spans, and then theoretically analyze their impact on detection. Our analysis shows that these spans increase the sentence complexity for detection, thereby making MGT detection intrinsically harder. Based on this finding, we propose a model-agnostic stacked enhancement framework that improves existing detectors by reducing the influence of hidden human-like spans. Specifically, we model span-level retention decisions as a latent-variable problem and instantiate the optimization with a hard-EM-inspired procedure, where the detector iteratively filters confidently human-like subsequences and refines itself on the remaining text. Extensive experiments across various LLMs and practical scenarios demonstrate that the proposed framework consistently enhances existing detectors. Notably, the framework can also work in a training-free manner, offering flexibility and scalability for practical deployment.