Phragmites is indeed invasive. We have become so used to seeing it in marshes that many of us have the impression that it's a natural part of the ecology (in North America). The biggest problem with it is that no other plants can grow where it is growing, so the insects that would feed on other plants are not present, the animals that would feed on them are not present, and so on.

Here's some more lucid information on the subject: http://www.massaudubon.org/saltmarsh/summary.php