Sadly, I think they do. That is, Facebook's terms include browsing Facebook with an accepted browser. That's nuts but it's also natural.
Facebook basically would like to pretend the browser is something like a "trusted client" rather than an inherent unknown.
It's a thing that you do pretending it's for security but, of course, it doesn't work for security but does work reasonably well for the masses aiming to view their own data in the way they like it.
Facebook stands by banning Robert Scoble for downloading the emails of his friend from his account using a script. The difference between a "browser" and "script" is completely arbitrary in the world of bits and bytes but banning "upsupported browsers"
