Context as well as the fact that she can understand people, so she must be able to process the difference on some level - she seems to know that people don't "have swords about the war on Iraq", for instance. And I get your Swedish example, but ð, θ, s and z are hardly allophones in German, are they? o.O Unless you're speech is impaired, and I'm pretty certain that people can tell the difference between those.

That kind of direct instruction you mention isn't foolproof, though, either, because it trains you to expect to hear certain things even if they're not there instead of training you to copy sounds the natives are making.
Fun fact: for the first two years I thought that "laugh" was pronounced with a kind of super-special θ rather than an f. I pronounced it by placing the tip of my tongue on my lower lip and my upper teeth between the two and got a mangled-sounding θʰ. Even though I must have heard my teacher and other learners pronounce a completely different sound countless times, that's how I had understood her instruction as to how to form that weird and alien sound, so I stuck with it. I could tell that there was a difference between how I and she pronounced that sound, and I knew I wasn't getting it right, but it took a while for me to figure out that it was just an "f", plain and simple.
So, while different approaches work for different students, I'm not sure this one'd do her so much good for her production. I think trying to make a meaningful difference is what really drove that point home for her here.