This study compares the impact of natural and synthetic data on training and evaluating large language models (LLMs), using the case of passive verb alternation in French and Italian. We use Blackbird Language Matrices (BLMs), structured datasets designed to probe linguistic knowledge of underlying patterns across sentence sets. We compare structured templates instantiated with natural sentences extracted from Universal Dependencies to structured templates of synthetic sentences. Experiments show that while models achieve ceiling performance when trained and tested on synthetic datasets, they do not reliably generalize to natural sentences. In contrast, models trained on natural data exhibit robust performance across both natural and synthetic test suites, demonstrating their superior ability to capture abstract linguistic patterns. These results corroborate the value of natural data and of structured set ups in linguistic evaluation for probing LLMs' syntactic and semantic knowledge.