Houses can be rented and apartments can be owned. Think of all the different local laws that might apply to someone that owns a condo, rents an apartment, owns a house, owns a townhome or rents any of these. Hell, even a HOA might have something to say about it. Then again you might rent from a person who doesn't care if you sub-rent out.

Having AirBNB try to determine if every single renter/homeowner has the rights would be a nightmare.

I'm not going to pretend I understand all the issues here but would you really want to be half pregnant here? I mean their users are violating all sorts of little laws in thousands of jurisdictions (all the cities/towns/counties/provinces/etc.) all over the world. In some cases this is bad form in some cases that's how BNBs work. I have a sort of feeling that it's better to take the "not my job" approach here rather than doing a half-assed job.

The problem, I suspect, is that people who own their homes are much harder for Airbnb to work with than people who are renting. Airbnb grew quickly by removing friction and making it very easy for people to list space and by providing the bare minimum support to people who list places. That was "good enough" for renters because they don't own the homes and don't care as much. Homeowners might expect a level of service that would tie up a lot of resources and hurt scaling.