It's totally true that any plant can become invasive -- I've always worried more about whether it's easy to control once it invades, and felt more comfortable growing something like a black sapote (big tree, easy to find an cut) than a bush or vine.
I confess I hate this particular bush -- one time I ordered black sapote seeds and started growing them in Thailand, only one sprouted. So I planted it out and watered it for three years, the whole time my in-laws kept complaining that it looked like a 'mahk-lawt', some word in the local dialect that I couldn't find in the dictionary. Finally it became painfully obvious that it was not a black sapote tree, and turned out to be this thing. At least I know now what its scientific name is.