JetJockey A4, you are correct. Both lateral and vertical positioning with WAAS/LPV is based upon satellite derived values including elevation. It is insensitive to altimeter settings, non-standard atmospheres (both hot and cold), etc.
In fact, whereas barometric altimetry is advertised to be +/- 50 ft (16m), WAAS vertical position accuracy is typically in the 0.5 m range.
With the imminent implementation of Galileo, not just North America, Japan and India but the entire world will have this augmented satellite navigation source thus permitting an "ILS-like" approach with localizer-like and glide-slope-like qualities to any airport in the world.
With GLS, a separate roughly $3 million box will be required near the airport - it too will provide the same level of accuracy, integrity, etc as WAAS/Galileo but will also require significant avionics improvements including VHF radios for the datalink, etc.
Hands down, WAAS/Galileo and LPV/APV is a far better solution for the aviation community anywhere in the world and for any size and type of aircraft.