Industrial image anomaly detection (IAD) is a pivotal topic with huge value. Due to the nature of anomalies, real anomalies in a specific modern industrial domain (i.e., domain-specific anomalies) are usually too rare to collect, which severely hinders IAD. Thus, zero-shot anomaly synthesis (ZSAS), which synthesizes pseudo anomaly images without any domain-specific anomaly, emerges as a vital technique for IAD. However, existing solutions are either unable to synthesize authentic pseudo anomalies, or require cumbersome training. Thus, we focus on ZSAS and propose a brand-new paradigm that can realize both authentic and training-free ZSAS. It is based on a chronically-ignored fact: Although domain-specific anomalies are rare, real anomalies from other domains (i.e., cross-domain anomalies) are actually abundant and directly applicable to ZSAS. Specifically, our new ZSAS paradigm makes three-fold contributions: First, we propose a novel method named Cross-domain Anomaly Injection (CAI), which directly exploits cross-domain anomalies to enable highly authentic ZSAS in a training-free manner. Second, to supply CAI with sufficient cross-domain anomalies, we build the first Domain-agnostic Anomaly Dataset (DAAD) within our best knowledge, which provides ZSAS with abundant real anomaly patterns. Third, we propose a CAI-guided Diffusion Mechanism, which can further break the quantity limit of real anomalies and enable unlimited anomaly synthesis. Our head-to-head comparison with existing ZSAS solutions justifies the superior performance of our paradigm for IAD and demonstrates it as an effective and pragmatic ZSAS solution.