Post hoc explanations have emerged as a way to improve user trust in machine learning models by providing insight into model decision-making. However, explanations tend to be evaluated based on their alignment with prior knowledge while the faithfulness of an explanation with respect to the model, a fundamental criterion, is often overlooked. Furthermore, the effect of explanation faithfulness and alignment on user trust and whether this effect differs among laypeople and domain experts is unclear. To investigate these questions, we conduct a user study with computer science students and doctors in three domain areas, controlling the laypeople and domain expert groups in each setting. The results indicate that laypeople base their trust in explanations on explanation faithfulness while domain experts base theirs on explanation alignment. To our knowledge, this work is the first to show that (1) different factors affect laypeople and domain experts' trust in post hoc explanations and (2) domain experts are subject to specific biases due to their expertise when interpreting post hoc explanations. By uncovering this phenomenon and exposing this cognitive bias, this work motivates the need to educate end users about how to properly interpret explanations and overcome their own cognitive biases, and motivates the development of simple and interpretable faithfulness metrics for end users. This research is particularly important and timely as post hoc explanations are increasingly being used in high-stakes, real-world settings such as medicine.