As an item used for transportation, it is first put under the Listed Property rules. That is why Publication 946 states that.
As the Instructions to Form 4562 point out, there are exception that can remove it from the Listed Property category. However, the tax code says that exception is if "substantially all of the use of which is in a trade or business of providing to unrelated persons services consisting of the transportation of persons or property for compensation or hire".
So the key phrase in that is "substantially all". The idea behind is that if there is any personal use, it is Listed Property. So things like buses, airplanes, trains, etc. would generally not be listed property because there is no personal use. If your vehicle is used ONLY for Uber, with no personal use, then you are right, it might qualify as non-listed property.
But as was pointed out, in most cases it probably won't matter anyways.
