Are large language models (LLMs) sensitive to the distinction between humanly possible and impossible languages? This question was recently used in a broader debate on whether LLMs and humans share the same innate learning biases. Previous work has answered it in the positive by comparing LLM learning curves on existing language datasets and on "impossible" datasets derived from them via various perturbation functions. Using the same methodology, we examine this claim on a wider set of languages and impossible perturbations. We find that in most cases, GPT-2 learns each language and its impossible counterpart equally easily, in contrast to previous findings. We also apply a more lenient condition by testing whether GPT-2 provides any kind of separation between the whole set of natural languages and the whole set of impossible languages, based on cross-linguistic variance in metrics derived from the learning curves. Taken together, these perspectives show that GPT-2 provides no systematic separation between the possible and the impossible.