We present PrivLEX, a novel image privacy classifier that grounds its decisions in legally defined personal data concepts. PrivLEX is the first interpretable privacy classifier aligned with legal concepts that leverages the recognition capabilities of Vision-Language Models (VLMs). PrivLEX relies on zero-shot VLM concept detection to provide interpretable classification through a label-free Concept Bottleneck Model, without requiring explicit concept labels during training. We demonstrate PrivLEX's ability to identify personal data concepts that are present in images. We further analyse the sensitivity of such concepts as perceived by human annotators of image privacy datasets.