Had the same discussion and a 20' delay as a result just a few days ago. Confusion came about as the FSO, FAM and TAB (ground staff policy direction) are written by three different authors, each with their own interpretation of the policy. The over-riding factor is that load control weight and balance supercedes the exit row requirement when the pax load is less than 50. Therefore, YES IT IS LEGAL to commit aviation with the exit rows vacant.
Not only do we require ABPs, yet each must agree to do so. Your kite may be (almost) full of ABPs, yet if they all say NO, even if encouraged so at no cost at the Service Desk or upon checkin, then we are obliged to operate with the exits bereft of ABPs.
Mobile (cell 'phone), online or kiosk checkin negates the acceptance of exit row seating. That's because the intended occupant needs to be sighted by checkin staff. If obese, on crutches or otherwise challenged, you will have to take a seat with a slightly shorter distance between your knee-cap and that of the back of the seat in front of you.
Funny request I heard once .. a pax in an exit row asking for an extension seatbelt.