A critical barrier to the trustworthiness of sixth-generation (6G) agentic autonomous networks is the uncertainty neglect bias; a cognitive tendency for large language model (LLM)-powered agents to make high-stakes decisions based on simple averages while ignoring the tail risk of extreme events. This paper proposes an unbiased, risk-aware framework for agentic negotiation, designed to ensure robust resource allocation in 6G network slicing. Specifically, agents leverage Digital Twins (DTs) to predict full latency distributions, which are then evaluated using a formal framework from extreme value theory, namely, Conditional Value-at-Risk (CVaR). This approach fundamentally shifts the agent's objective from reasoning over the mean to reasoning over the tail, thereby building a statistically-grounded buffer against worst-case outcomes. Furthermore, our framework ensures full uncertainty awareness by requiring agents to quantify epistemic uncertainty -- confidence in their own DTs predictions -- and propagate this meta-verification to make robust decisions, preventing them from acting on unreliable data. We validate this framework in a 6G inter-slice negotiation use-case between an eMBB and a URLLC agent across 200 trials. The results demonstrate the profound failure of the biased, mean-based baseline, which systematically violates the strict URLLC SLA 11 times. Our unbiased, CVaR-aware agent successfully mitigates this bias, eliminating SLA violations entirely and significantly reducing the 99.999th-percentile latencies by up to 51.7\%. We show this reliability comes at the rational and quantifiable cost of reduced energy savings, exposing the false economy of the biased approach. Crucially, executing our framework with an otel-llm-1b-it model on a single NVIDIA RTX A4000 GPU achieves sub-1.5-second inference times, validating the feasibility for non-real-time RIC use-cases.