I was told that if I am claiming to have a disability (which, I could go this route, since I do have a condition related to pain and lower-back and lower-body movement, though never really needed to put the two and two together since I've never been told in the 16 years I've had it that I couldn't sit on a freakin' floor somewhere), I could most likely get a reasonable accommodation, which would involve being allowed to sit on a specific place on the floor where the library people permitted me to sit during the visit and involve the staff informing all the other staff that I was allowed to be there. Uh, yeah, no thanks. I did ask for the person to e-mail me about looking into an accommodation though, because I'm really curious as to where this does or doesn't go.
The BPL website only says that blocking the aisles by sitting or lying in them is not permitted, not that no one can ever sit on any floor. It also doesn't say anything about prohibiting chairs, books, shelves, carts, potted plants, walls, toilets, backpacks, etc. that blind people could also trip over, because I assume the person who made the policy is aware that blind people are always prepared for the possibility of all different types of moving and stationary objects, just like anyone else.
I suspect that, like many things, this is an anti-people-with-persistent-mental-illness issue, aimed at behaviors common to people who tend to be tired, confused, medicated, sleep-deprived, etc. I've also heard, less recently, of BPL security guards telling people who fit this demographic that they need to have a book open in front of them or else they're "loitering."