I think Yamaha only calls it a "Sports bike". The problem is its named a "YZF-R3", kinda associating it with the R6 and R1. I personally didn't see any problems with it, only one insurance quoted me 1200$ because its a YZF but my other quotes were around the same as a ninja 300 or a cbr300. I would say shop around or call them up.
As evidenced by the above comments, insurance companies don't necessarily go by the vehicle manufacturer's marketing classification. They have their own methods and formulas for defining the classification of a particular vehicle.
The make, model and manufacturer's own classification are variables, but so are engine size, number of cylinders, height, weight, horsepower, parts availability, and whatever else a particular insurance company decides is important to include in their formula.
So Yamaha can call it whatever they want, and insurance companies will go ahead and classify it however they decide.
Liability should be cheap, but other coverage is probably ridiculous due to:
1. It being a bike for new riders (meaning that they will probably get into more accidents than larger bikes)
2. The blue book value of the bike being lower than that of other bikes (meaning that more get totaled for the same amount of damage that wouldn't total a more expensive bike)
3. There not being a ton of data on this particular model (since it is new)
It was the exact same price on insurance as the RC390 through Allstate, and that bike has standard ABS, and cheaper than a CBR500R with ABS. I think they just pull a number out of a hat, a hat with all high numbers in it that is.
The term Super Sport means something different world wide than in this country. As previously said, it is what the bike was designed to do. Here it simply means 600 sportbike, but even that is smeared between the manufactures. Yamaha calls all of their sport bikes super sport, not differentiating between R1, R6, R3. Whereas Kawasaki refers to their Ninjas as Super sport and Sport. Go figure? FZ6R is a sport because it isn't a YZF, now isn't that clear.
A note about the KTM RC390, it was never designed for anything more than track riding (noting large rear tire, exaggerated riding position, very small petrol tank, and rock hard seat). I think most of us want a bit more comfort than it affords for hitting the back roads.