In weight paint mode, these bones do bear any influence on such areas (the areas are dark blue when the particular bones are selected) yet these parts deforms entirely or in part when the bone is posed. The model was done on Maya (and Zbrush) and both FBS and OBJ imports were tried with the same behavior. I rigged it using the Rigify metarig. The blend file is available here: https://goo.gl/MznE7J
Left Side Problem. Right Side No Problem.
An example would be posing the upper arm bone which results in the glasses frame and eye deforming as well