I filled out the (slightly broken) form to be safe, and am happily continuing to fill out the actual application as well. I figure it's fairly safe to submit rec letters through the mail, because every other school I've applied to has provisions to do so.
...Duh, I misread the check thing. Only thing that has me still worried is that the page says it's $80 in one place and $50 in another. Guess we'll find out when I submit the application...