It's about cities like NYC that have less than one percent vacancy rates, where a couple of AirBNB related effects put upward pressure on rents:
1) A person can stay in an apartment they wouldn't otherwise be able to afford, pushing rents up (I personally know several people who maintain apartments like this, either by leaving for a couple days per month or maintaining an apartment after moving out of town.)
2) A full apartment stays off the market because it is being used as a dedicated hotel
Both of these make a difference in rent prices, though it's hard to say how much.
I'd be happy to see a ban on AirBNB while residential vacancy rates are lower than 3%. I love the service but not what it does to my already pretty unaffordable city.