Please note that there are two sides to being "invasive". There are invasive roots (which as you said may be contained in a pot) and there are invasive seeds which blow around or get carried away by wildlife (birds, etc.).

Ruellia brittoniana (mexican petunia) is considered a Category 1 (highest) invasive plant in Florida, but that doesn't mean it is true for NC. Their statement:

This warning applies to all parts of the state of Florida (and other areas with similar mild climates). Where hardy, the Mexican petunia excels at invading wetlands.

Knowing this information and the scientific name will allow you to search for information about your area.

Here is a link that might be useful: source

Babylou,
From what I understand, Mexican petuna is only cold hardy down to zone 8.
It may die this winter in your zone, depending on the temps this winter where you live.
Mulch it real good.
The entire stalk died for me in the winter and I cut it down to about 3 inches high.
It was mulched real good and it was fine over the winter, but we had a warm winter this year.
I am close to Augusta, Ga in zone 8.
If you like the plant, I would dig it up and pot it up in October and move it into a shed or garage so it survives.
They are the most beautiful plants, mine are blooming already. They will bloom all summer til frost, which for us is usually the beginning of December.

It's definitely aggressive (no wavering on that adjective).

Esh_ga7, you didn't mention that any stems that come in contact with the soil (the long stems bend and flop) will also root at their nodes, bolstering the choking-out ability of a thicket of Mexican petunia in a landscape.

I'd say aggressive, definitely. i haven't had it reseed for me but it does spread underground, quite determinedly. I have it planted in hard clay up by the road where it gets no extra water and it's doing just fine. I wouldn't put it in fluffy soil where it got water or it'd take over! It's nice b/c the foliage is pretty and neat and it blooms from june or so til frost. Mine always dies back to the ground, which is good b/c by the end of the season it's 2- 2.5' high.

It is a gorgeous plant and yes invasive (in Florida, from what I know). At HD in Florida, they have a Florida friendly variety. I bought several 3 years ago, and they have not spread. It is sterile, and cannot spread. If you can get your hands on those you won't have to worry!! Plus, they're cheap :) Christy

I have had a couple plants for about ten years and have never had any problem with it. It is in hard clay. I live a little west of Columbia, S C.

Yes, it is invasive. Only plant it in a pot or in an area bordered by driveway, sideway, etc- because the roots reach in all directions like snakes. I never had a problem with flowers or seeds spreading the plant in Charlotte.
If you take a mexican petunia plant out of the ground... cut off the greenery and leave the roots in a bucket for a month or two... you can still plant the roots and they will grow. The root is almost indestructible. That is both reliable and a huge warning.
If you want to clear a bed of mexican petunias you'll have to dig it out DEEP to get all the root fragments. If you still want to take a shot, you should be fine if they are contained. I planted them in front of a kitchen bay window instead of shrubs, and they looked great all summer. I placed japanese iris thickly in one corner, dianthus in another. LambsEar and gerber daisy along the front wooden border. Each plant held its own, but every year expect each to get more and more dense. You may cut the plants back in height to make the plant fuller. Every winter they die back but they will return.
The more sun the mexican petunia gets, the more it blooms.