i am not sure, but i think the basic answer to your question is no, they do not have a block of tickets like colleges do for the visiting team.
i think, and again stress think, that a certain number of tickets are available for the visiting TEAM to purchase, not visiting fans.So people like players family, friends, coaches family can attend. If those are not sold they are returned to the home team and go on sale to the general public through the home team.
Having said that, for the Miami game i would be shocked if there is not an established Bills group that goes every year and has tickets. Check the Bills Backers sites and inquire, think you will be pleasantly surprised.