Either Sprint is blocking LTE connections, which happens, or there is an issue with your device. Have you made sure your GS3 is in CDMA/LTE mode? Have you tried cycling through airplane mode to force your device to scan for LTE? Have you been able to connect to LTE in other areas? If you can connect in other areas, but not the site, then Sprint isn't allowing connections.
There are several places where this has occurred. There were several sites in Kansas (around Newton and Wichita) that Sprint didn't allow connections to for weeks even after all the sites around them went live, showed up on coverage maps and the area was formally launched.
Robert