Certain example embodiments of this invention relate to vacuum insulated glass (VIG) units. The VIG unit may comprise first and second substrates with inner and outer substantially planar surfaces. For either or both of the first and second substrates, when considered along a side cross-section, a portion of the inner planar surface is removed proximate to an outer edge of the glass substrate so as to form a shoulder portion. An inner surface of the shoulder portion is angled (a negative number of degrees, zero degrees, or a positive number of degrees) relative to the inner and outer planar surfaces. The shoulder portion at its smallest height is at least about 50% of the glass substrate at its largest height. A side portion of the step proximate the edge also may be angled, e.g., so that it is or is not perpendicular to the planar surfaces.