Automating chest radiograph interpretation using Deep Learning (DL) models has the potential to significantly improve clinical workflows, decision-making, and large-scale health screening. However, in medical settings, merely optimising predictive performance is insufficient, as the quantification of uncertainty is equally crucial. This paper investigates the relationship between predictive uncertainty, derived from Bayesian Deep Learning approximations, and human/linguistic uncertainty, as estimated from free-text radiology reports labelled by rule-based labellers. Utilising BERT as the model of choice, this study evaluates different binarisation methods for uncertainty labels and explores the efficacy of Monte Carlo Dropout and Deep Ensembles in estimating predictive uncertainty. The results demonstrate good model performance, but also a modest correlation between predictive and linguistic uncertainty, highlighting the challenges in aligning machine uncertainty with human interpretation nuances. Our findings suggest that while Bayesian approximations provide valuable uncertainty estimates, further refinement is necessary to fully capture and utilise the subtleties of human uncertainty in clinical applications.