Large language models (LLMs) are increasingly used to support scientific work, but it is unclear whether they uphold responsible conduct of research (RCR) norms or help undermine them. We introduce SciIntBench, an adversarial benchmark of 810 prompts across ten RCR categories and three scientific domains. Each scenario appears as an Overt Adversarial, Covert Adversarial, and Benign version, allowing us to jointly measure framing-sensitive refusal of misconduct and helpfulness on legitimate requests. We evaluate 16 commercial and open-weight LLMs from six providers (2024--2026), producing 12,960 responses. We find that scientific integrity alignment is strongly framing-sensitive: models refuse explicit misconduct far more reliably than covert violations, especially failing when misconduct is presented as a pressure-driven shortcut. Refusals vary by RCR category, with weaker boundaries around transparency, plagiarism, and fabrication.