Hithere, TG. Actually, all Tradescantias are native of the Americas. One can debate which area they may or may not have inhabited at a certain point in time, but plants do creep on their own and are 'moved' by animals, storms, as well as being moved around by people, so I'm not sure about calling something native to Mexico invasive in TX, for example.
But the Callisias are not all thought to be native, though many are of dubious, debated origins, and as a whole, this is a mysterious group of plants because of the lack of info readily available. That would also explain the confusion over the origins of some - hard to decide that if the ID is still in question. Without a magnifying glass and checklist of characteristics, they look alike, but when there's different colored and shaped leaves, and the presence of flowers on one and not the other, that's a lot of difference. C. repens does bloom, but not abundantly and regularly like this other plant. When it does, it looks identical. USDA plants database has no pics and says C. repens is native to Virgin Islands and Puerto Rico but introduced in the lower 48. They completely ignore Mexico, so I don't consider C. repens not native, especially with all of the confusion about the ID, though some purists might.
I've put a lot of hours into trying to ID this plant, and get a handle on Callisias in general. I've not found a single reliable resource with comprehensive info about them, except in writing, those paragraphs of abbreviated jargon that I don't understand. Tracing the origins of the few pics found at supposedly reliable resources is usually maddening since the same image will be shown on a multitude of sites. Writing to the professors, scientists, webmasters, usually results in finding out that nobody knows who took the pic, or when, or where...
It's likely that Gin's plant is the same "not C. repens." I got this plant from DH's Mom's yard. Then I noticed the little mom'n'pop store that sells plants had made a weak effort to use some of this stuff on a wire topiary frame, and bits of it are in many of their pots, and the ground around the plant stand tables. After curiosity has gotten to this level, I've seen it other places NOT in pots as a 'house plant.' It's around readily up here, so I imagine its' survival farther south would be even more spectacular.
Smiles!
