Neither of those sources are showing Sagittaria as an invasive. The first one ( University of Florida) is a list aquatics "and invasive". Not all the plants listed are invasive.
The page you reference at invasives.org is just a list a Sagittaria. If you go to this page and click on either Federal Noxious Weeds or Aquatics you will only see Sagittaria sagittifolia list. It is not a US native. If you click on State Noxious Weeds you will see that one plus Sagittaria graminea, which is only listed as noxious in Washington State.
http://www.invasive.org/specie...
Thats not to say that other species are not aggressive, they are just not considered invasive, which is a term used to describe species (usually not native to a particular area) which disrupt the natural ecosystem.
