If anyone looks at old topics, should be noted that the real pampas grass(Cortaderia selloana) can't even grow in Iowa, which is native to the Argentina pampas. I tried growing a special cold hardier cultivar of it, mulched it too, just fizzled away after awhile, think that one was zone 6, and regular is at least zone 7 for plant hardiness.
There is also a grass that is called hardy pampas grass(Saccharum ravennae), and seed source is critical for that, some is zone 6, but can get some zone 5 plants. That is also a clumping grass and I doubt it is invasive in areas where it isn't fully hardy. It doesn't run and does not flower early enough for viable seeds. Its leaves are a few feet tall, but what is special about this plant is the plumes that rise way above the leaves.
I have a feeling from what I read, that the running Miscanthus sacchariflorus was the grass talked about in this topic. It has white plumes, so I guess I could see why sometimes it could be called that, but is why botanical names become important.
Not 100% sure, but I've read doesn't even seed here and have not seen proof that it has either, so is only locally aggressive where planted. Is one of the parents to that Giant Miscanthus a lot of people are planting.