Can in-context learning (ICL) override pre-trained label semantics, or does it merely refine an existing semantic backbone? We address this question by treating LLMs as prompt-induced classifiers and contrasting their behavior under \emph{natural} demonstrations (with correct labels) and \emph{inverted} demonstrations (systematically flipping label meanings). We decompose ICL behavior into three alignment metrics (truth, prior, and prompt alignment) and introduce a semantic override rate, defined as correctness under flipped semantics. Across eight classification tasks and eight open-source LLMs (1--12B parameters), we find consistent evidence for a semantic anchor view. With natural demonstrations, ICL improves accuracy while maintaining strong prior alignment; most correct predictions coincide with zero-shot behavior, even when the prior is weak. With inverted demonstrations, models cannot learn coherent anti-semantic classifiers: prompt alignment increases only by sacrificing accuracy, and semantic override rates remain exactly zero in our few-shot 1--12B setting. Rather than flexibly remapping label meanings, ICL primarily adjusts how inputs project onto stable semantic directions learned during pre-training, clarifying fundamental limits of few-shot prompting and suggesting that overriding label semantics at these scales requires interventions beyond ICL. All code is available at: https://github.com/AnanthaPadmanaban-KrishnaKumar/semantic-anchors-icl.