Large Language Models (LLMs) offer promising avenues for methodological and applied innovations in survey research by using synthetic respondents to emulate human answers and behaviour, potentially mitigating measurement and representation errors. However, the extent to which LLMs recover aggregate item distributions remains uncertain and downstream applications risk reproducing social stereotypes and biases inherited from training data. We evaluate the reliability of LLM-generated synthetic survey responses against ground-truth human responses from a Chilean public opinion probabilistic survey. Specifically, we benchmark 128 prompt-model-question triplets, generating 189,696 synthetic profiles, and pool performance metrics (i.e., accuracy, precision, recall, and F1-score) in a meta-analysis across 128 question-subsample pairs to test for biases along key sociodemographic dimensions. The evaluation spans OpenAI's GPT family and o-series reasoning models, as well as Llama and Qwen checkpoints. Three results stand out. First, synthetic responses achieve excellent performance on trust items (F1-score and accuracy > 0.90). Second, GPT-4o, GPT-4o-mini and Llama 4 Maverick perform comparably on this task. Third, synthetic-human alignment is highest among respondents aged 45-59. Overall, LLM-based synthetic samples approximate responses from a probabilistic sample, though with substantial item-level heterogeneity. Capturing the full nuance of public opinion remains challenging and requires careful calibration and additional distributional tests to ensure algorithmic fidelity and reduce errors.