Well, I think maybe I found the answer. Calling T-Mobile was no help.
I did find a thread floating around on the net somehwere. I cannot seem to locate it.
But the bottom line (and please excuse me if I mess up some of the technical details as I am not a guru...) is that, at least the international GS3 I9300 phones do not operate on the 1700 band that T-Mobile USA uses for its high speed data network. The phone then mistakenly thinks it is roaming....but in reality it isn't truly roaming, it just can't find the high speed network and throws up the roaming notification.
T-Mobile is apparently moving the high speed data to 1900, which the phone can handle just fine. I'm guessing that is why my phone worked fine in Chicago, no roaming, with the HSDPA at full speed. My guess is that Chicago area has already been switched to 1900, which is why everything worked normally.
So, I hope maybe this helps people out some. I simply turned on the data while roaming feature as I know that I am in T-Mobile data coverage area, so I'm not worried about it. It only runs at EDGE speeds though.