Actually Sharon, that raises a very good point. Most people don't take care of plants as much as you or I do. Especially with ground covers. So, when choosing a ground cover, it is important to choose one that is not going to invade local flora and fauna.
I always say this, and I'll say it again: it's really important to check your local invasive lists (usually found at a government website but, easy to look up by just typing in your state or province AND invasive list). Anyway, just because something is not on an invasive list does not mean that it isn't a huge problem.
Government postings are definately NOT up to date. For this reason it is a good idea to acquire as much knowledge about a particular plant from experts as you can before planting it.
A huge problem where I live is Scotch Broom that was planted by a Scottish person who brought the seeds because they were lonely from their homeland. Well, now the entire Island is covered with the stuff because someone planted a few seeds. Another example is English Ivy, around where I live all the forests are 100% invaded with the stuff. It has choked out all native flora, which directly impacts local fauna.
We gardeners have to be very careful and very informed before planting certain plants so it is important that we listen to advice given to eachother and take it to heart.