What she's saying is that there is no known practical test which requires string theory as an explanation -- the other theories are sufficient. That doesn't contradict the idea that there are tests which could disprove string theory.
Consider the claim that a man who stands before you was created just outside your front door 5 minutes ago, fully formed with enough knowledge to communicate and a local accent, etc., but no evidence of any prior existence was created along with him. Your alternative explanation is that he's lying and was born 30 years ago, as his appearance suggests. You could disprove his theory by finding his house with pictures of him growing up -- that's prior evidence of his existence. It's extraordinarily doubtful that you could ever prove his claim, even if it were true -- it's just much more likely by virtue of simplicity that he was born and you can't find evidence of where he grew up prior to 5 minutes ago, because there's certainly no less evidence of that.
It's not enough for a theory to stand up to attempts to disprove it -- that's a necessary but insufficient condition. It also has to explain something, anything, in a way that is either simpler or more complete than other known theories.
Newton's Laws stand up because they are simpler but less complete than theories like relativity. Relativity stands up because it is more complete than Newton's Laws -- there are known situations when Newton's Laws simply give the wrong answer and relativity gives the right one. QM stands up because it explains something that relativity does not, so it's more complete in a different sense. Aristotelian cosmology failed because it was simply wrong. Geocentrism failed not because it was "wrong" (a geocentric frame of reference is a perfectly valid, albeit non-inertial, frame of reference, and you can absolutely make accurate calculations about the universe with Earth defined as its geometric center), but because it was incredibly complicated compared to heliocentrism and provided no discernible scientific benefits. That leads to the question: is string theory like geocentrism, in that it's not strictly disproven but it's an unnecessary pain in the ass?
The request here would be for a situation that String Theory explains, and QM and Relativity either do not explain, or explain inaccurately, or explain in a more complicated fashion. It's useless until it provides one of those things, other than the joy of pure mathematics. Science does not state "all proposed theories are true until disproven" -- rather, it says "don't assume a proposed theory is true until you fail to either disprove it, or come up with an easier answer".
I'm not personally in a good position to evaluate the merits of string theory anymore, and neither is anybody with merely the knowledge in that wikipedia article (though it helps). You should note, though, that the wikipedia article you yourself cited, cites Feynman, Penrose, and Sheldon Lee Glashow as making an even stronger argument Jane Q. Public is making -- saying that it simply is a failure as a theory, because it doesn't provide practical novel experimental predictions (in other words, it's not more complete than existing theories).