The vertical tail is NOT the reason for "skewing" (I assume you mean crabbing) in crosswind landings. The answer is directional stability. But first, let's take a look at why crosswind landings are a problem.
Aircrafts fly relative to the air
Aircrafts fly in the air. They fly in a way such that the air pressure is balanced around the aircraft. Thus, if there is a 100 knot perfectly steady wind, any aircraft would fly just fine. A ground observer would see a 100 knot difference in the aircraft's velocity vector, but the relative movement between the aircraft and its surrounding air is exactly the same as a no-wind condition.
Try moving around a train. The train is travelling at 50 mph, yet you can move around the cabin just like on the ground.
Now if some pilot is going to land, he must transition from travelling through air to travelling on the ground. That's when the problem arises. His ground track must be along the centerline of the runway, and he must be pointing in the same direction as his ground track as well.
Back to the train analogy, try jumping from a 50 mph train to the ground. It's difficult because you have to match the 2 movements: one relative to the train and another relative to the ground.
Now we understand that aircrafts move through steady wind just as they do in still air. If a crosswind is 20 knots from the right, the B2 would be drifting to the left at 20 knots if its heading is exactly the same as the runway.
Let's assume what you said is true: on a B2 (which has no vertical tail), the aircraft is not affected by crosswind, and thus can land by pointing the nose straight at the runway.
Then it logically follows, that a crosswind of any magnitude would have an neglectable effect on the aircraft. Which also means, if the aircraft starts floating left or right, there is no way the pilot can control it! He can hold winds level and a constant heading (say 360), but the aircraft may drift sideways!