I have a hard time believing that, too. The Snapdragon S3 is a larger SoC and significantly slower than the S4 Krait. While there is a difference between the International and US SoC footprints, making a separate one solely for T-Mo USA seems asinine, as it (again) would require a different manufacturing process. Especially to put in a year-old SoC that doesn't perform nearly as well.
I would believe that T-Mo USA is purposely spreading misinformation so that their customers do not ask questions about LTE compatibility. My coworker that has the T-Mo USA GS3 is out of the office, but I'll ask him to look at his specs. I don't think a Snapdragon S3 would be able to keep up with the demands of the GS3. I have an Evo 3D (that uses the CDMA version of the chip - 8660) and there is no way it could run TouchWiz Nature UX.
And I moved our discussion to the T-Mo thread, it's more appropriate than the Sprint one.