The only way that could possibly be true is if the price the scalpers charged was the face price they had to pay.

In that world, there wouldn't be scalpers.

Are you unaware that scalpers are set up to hoover up as many tickets as possible before an actual person that wants to visit the event can get one? Because it seems like you are?

I'm aware. But I'm also aware that in the absence of customers, the scalper's prices will fall to zero.

If the scalper has enough customers that he can sell out the show above the face price of the tickets, the existence of those customers is sufficient to make it "practically impossible to get a ticket at face price" whether the scalper exists or not.