That's a funny point, but consider this: Land (along with regulation) is what limits the supply of housing in SF. If you transform a house to a hotel, then yes, it's true, the supply of housing has fallen. However, at the same time, the supply of hotels has risen. If the world equilibrates, then perhaps a hotel is torn down elsewhere and its land is freed up for housing. So I don't think it's necessarily the case that short-term rentals drive up the price of long-term rentals (but perhaps it is once you acknowledge that hotel rooms have higher density than AirBnB).
Also, it seems like this logic could apply to anything. Oh, you're building a Chipotle so that poor people can eat cheap food and earn money? Well that Chipotle takes up land, driving up rental prices. High rental prices means that people have less money and less of a budget for food. So the justification is: "San Francisco residents are so poor, they need the ability to become drive up prices and become even poorer!" But that seems a bit silly.