So right after I posted my question, I played around on the site a bit more and found the online chat option. Asked them there - they said exactly what you did - you have to call to find out the fare class. HOWEVER, they did say that if you call to book a ticket by phone, the fare will be different than what's online! Can't figure out for the life of me why that would be, but hey when you're getting airfares as cheap as they're advertising, can't really ask questions can you?

Interesting that fare class doesn't matter to some of you. Here it's the question of earning 0% or 25% vs 100% of flown miles - especially for us mileage accruers/redeemers, makes a world of difference.