It is true that 37signals emphasizes making the lives of their customers easier. To a fault.
But I don't see how the password recovery feature would be any less easy and convenient if it consisted of sending an email with a password reset link that brings you to a page where you just enter a new password twice and get logged in immediately. You have to deal with password reset link expiry and such but no big deal.
I can come at this from the other end: part of my consulting deals with end-users on a daily basis, and I've seen even novice users _finally_ starting to use multiple passwords on their own without prompting.
So, it more likely would be a simple case of their forgetting which password they used on that particular system.
But I don't see how the password recovery feature would be any less easy and convenient if it consisted of sending an email with a password reset link that brings you to a page where you just enter a new password twice and get logged in immediately. You have to deal with password reset link expiry and such but no big deal.