I think Mike is correct. They must have time to check the passenger manifest before sailing.
As for the price...........we always book the cheapest outside or balcony room on the ship and never pay more than $100 pp/day including port and taxes. Our upcoming cruise on the Sovereign is $84.75 pp/day. Yooooooohooooooo! That is $122 total savings over what we consider a bargain. It'll all end up on the craps table though.