This claim is at best a confusing one. I mean, okay, I might buy the idea that science can only be the detector of certain things, but what on Earth does she mean by that? If we are talking about the supernatural, then by definition, I'd have to agree. Supernatural things are "beyond nature"... of course, things may be beyond nature because of some particular quality the object possesses, or because of our currently limited technology. We don't have the ability to detect quarks directly, only indirectly, for instance. Will we ever be able to detect quarks directly? I don't know. If you had told someone a millennium ago about quarks, they probably would have assumed you were talking about the supernatural, something that was impossible to detect, even indirectly. If the supernatural interacted with the physical world, science should be able to detect it through its effects on physical objects. Of course, if the supernatural we are talking about is truly undetectable even indirectly (a.k.a. god), what is the difference between that, and god not existing?
As for the examples given, none of these are supernatural phenomena, and they are all things which humans detect pretty reliably every day. And science actually does a pretty good job of catching a lot of cases that even we can't detect, like when a person is lying, through changes these emotions make in our bodies or our brains. We are detecting these emotions indirectly, but is this really any different than detecting quarks? I don't see how. And before we talk about memory or thoughts, we should define what we mean by them, because neuroscience tells us that neither are the unified things we believe them to be. But can we detect them? How else would we know how memory or thinking works in the brain, even a little bit? What does she thick the entire fields of psychology and neuroscience are about?
What else can science detect that doesn't consist of physical matter?
Clearly, the claim that non-physical entities are beyond the detection of science is false.
And even if the claim was true, that only leaves open the possibility that a god could exist, it does not prove that one does exist.