This paper investigates the accuracy of Augmented Reality (AR) technologies, particularly commercially available optical see-through displays, in depicting virtual content inside the human body for surgical planning. Their inherent limitations result in inaccuracies in perceived object positioning. We examine how occlusion, specifically with opaque surfaces, affects perceived depth of virtual objects at arm's length working distances. A custom apparatus with a half-silvered mirror was developed, providing accurate depth cues excluding occlusion, differing from commercial displays. We carried out a study, contrasting our apparatus with a HoloLens 2, involving a depth estimation task under varied surface complexities and illuminations. In addition, we explored the effects of creating a virtual "hole" in the surface. Subjects' depth estimation accuracy and confidence were assessed. Results showed more depth estimation variation with HoloLens and significant depth error beneath complex occluding surfaces. However, creating a virtual hole significantly reduced depth errors and increased subjects' confidence, irrespective of accuracy enhancement. These findings have important implications for the design and use of mixed-reality technologies in surgical applications, and industrial applications such as using virtual content to guide maintenance or repair of components hidden beneath the opaque outer surface of equipment. A free copy of this paper and all supplemental materials are available at https://bit.ly/3YbkwjU.