Unvetted scientific claims about vaccines can spread rapidly and undermine decades of progress in immunization and public trust. A recent non-peer-reviewed analysis, promoted at political hearings, in the documentary "An Inconvenient Study," and on social media, has been used to suggest that vaccinated children experience higher rates of chronic illness than unvaccinated peers. Despite standard regression models, critical flaws - uncontrolled confounding, exposure misclassification, unequal follow-up, and outcome multiplicity, invalidate causal inference. An independent group of international experts critically appraises this analysis and contrast its claims with the consistent evidence confirming vaccine safety and effectiveness. We also show how poorly designed studies can distort public discourse, amplify misinformation, and fuel vaccine hesitancy. We outline actions to strengthen research integrity, such as transparent data sharing, labeling of non-peer-reviewed content, and evidence-based communication. Safeguarding public health demands that vaccine evidence be methodologically sound, reviewed, and interpreted by qualified experts.