So no, they're not really pushing up the costs of rental apartments, because they're not in that market segment at all.
But that doesn't mean I'm shrugging my shoulders and saying "eh, that's what disruption looks like!" when renters in apartment buildings convert their spaces into mini-hotels. That's abusive. Fortunately, it's also unlawful, and there's a clear chain of responsibility to resolve it.
Cotenants in buildings experiencing Airbnb abuse shouldn't bother talking to Airbnb or their neighbors. They should report the conversion to their landlord, and then have a notice-and-cure drafted. In most circumstances, landlords probably cannot allow their buildings to be partially converted into hotels under the terms of their existing tenants leases.