I also used to own a Chevy Tracker (1999) with the separate transfer case gear shift stick. I researched and hunted for a newer Suzuki Grand Vitara. As you see in my signature, I got one.
In my research, the excerpt you quoted is correct. Only the four-mode 4WD is flat-towable. The car needs to have a 4WD dial (no longer a gear stick). Some ads may state that the car is 4WD, but watch out...the single-mode 4WD does not have this dial and is not flat-towable.
Take a look at the pics in this craigslist ad:
Grand VitaraLook at the pic with the automatic gear shift. Just in front of that are several dials. The four-mode 4wd dial will be in the lower left. This car doesn't have it, but you can see where the space is for it. Anyway, that's what I always looked for to make sure the car was flat-towable.
As always, it is best to read the owners manual of any car you are considering purchasing to make sure it states that the car is towable on the ground behind a recreational vehicle. Look in the index for "Recreational Towing". Usually what you find under just "Towing" is for a breakdown (i.e. road service).
2002 Itasca Suncruiser 32V
2012 Suzuki Grand Vitara