Large language models are increasingly used to support organizational decisions from hiring to governance, raising fairness concerns in AI-assisted evaluation. Prior work has focused mainly on demographic bias and broader preference effects, rather than on whether evaluators reward expressed trust in AI itself. We study this phenomenon as LLM Nepotism, an attitude-driven bias channel in which favorable signals toward AI are rewarded even when they are not relevant to role-related merit. We introduce a two-phase simulation pipeline that first isolates AI-trust preference in qualification-matched resume screening and then examines its downstream effects in board-level decision making. Across several popular LLMs, we find that resume screeners tend to favor candidates with positive or non-critical attitudes toward AI, discriminating skeptical, human-centered counterparts. These biases suggest a loophole: LLM-based hiring can produce more homogeneous AI-trusting organizations, whose decision-makers exhibit greater scrutiny failure and delegation to AI agents, approving flawed proposals more readily while favoring AI-delegation initiatives. To mitigate this behavior, we additionally study prompt-based mitigation and propose Merit-Attitude Factorization, which separates non-merit AI attitude from merit-based evaluation and attenuates this bias across experiments.