Cross-view video representation learning aims to capture viewpoint-invariant action semantics despite substantial appearance changes across egocentric and exocentric videos. However, existing methods encode each video as a unified embedding, where view-invariant and view-variant semantics inevitably entangle under co-occurrences — a failure mode we show persists even in cross-view methods explicitly trained for view-invariance. Our key insight is that a view-invariant feature is truly disentangled when it can be sufficiently recomposed with an arbitrary view-variant feature while preserving their independent semantics. Building on this, we propose PRISM, that decomposes video into view-invariant and view-variant latents and recompose them under language supervision encouraging clean decomposition of the two streams. PRISM achieves state-of-the-art results on EgoExo4D, EgoExoLearn, AE2, even surpassing in-domain models under zero-shot setting. Code is available at [https://github.com/litcoderr/prism](https://github.com/litcoderr/prism).