It must be very different in the US... I often got put in places I simply cannot physically sit: I'm tall, have a lot of muscle and am overweight. All three not to the extreme, but i'm taller than most (I'm Dutch, close to 2m), my shoulders are wider than most and my lower body is large enough to fit 'snug' in a seat (but not hanging (over)). The tall part is the biggest issue here. In 'middle seats' on most airlines, I simply cannot fit; I cannot possibly sit there without putting my legs at both my neighbors. The normal response of the attendents usually was to move someone smaller from exit seats to mine. As I cannot sit and next to that I will cause discomfort to both my neighbors.

That said, now I just book exit seats or comfort seats, but when those are full this still happens. Some airlines, like Vueling, I just don't fly with anymore as they made the seats so small that most seats are too small to fit tall people in at all. But they also moved me to exit seats when that was the only flight I could take.

When there are obese people, they are routinely moved to business class (on inter europe flights; never saw it on an international flight) or exit seats; I saw this on Easyjet, Ryanair and BA. I haven't seen your situation occur here; I would refuse to fly to be honest. Just get the pilot out and ask his opinion; they have the last say. If you cannot sit (and if a quarter of your space is filled with someone else, for me that means I cannot sit), the pilot will agree it's not a safe situation for you.