As AI-generated and AI-assisted content floods online spaces, source labels attached to such content can distort human reasoning judgments, with downstream consequences for moderation, evaluation, and decision-making. Whether LLMs share this vulnerability, or offer more source-agnostic evaluation, remains an open question with direct implications for human-AI collaboration. We examine this issue using logical fallacies as a controlled setting to isolate source-label effects on reasoning quality, independent of domain knowledge. We conduct an online study (N=505) where participants are assigned to a source condition (human, AI, human with AI assistance, AI with human assistance, or no disclosure) and evaluate comments containing logical fallacies, comparing their judgments with those of LLMs (GPT-5.2, Gemini 2.5 Flash, Claude Sonnet 4.5), who were evaluated across the same source conditions. Human evaluators were significantly more susceptible to fallacies labeled as written by human or human with AI assistance and assigned higher trust and evaluation ratings in these conditions. LLM evaluations remained comparatively stable across source labels, though performance varied across models. Confidence levels were similarly high across conditions for both humans and LLMs, regardless of fallacy presence. Our findings indicate that source-label bias in reasoning evaluation is primarily a human vulnerability and highlight the potential of human-LLM collaboration in increasingly AI-mediated environments.