For the purposes of this discussion, I do not intend to make a hard distinction between "science" and other intellectual contexts in which we discuss "facts" - e.g. history. For instance, it is a fact that John F. Kennedy was assassinated. Facts of this kind fall within the context of "science," broadly construed as our best effort to form a rational account of empirical reality. Granted, one doesn't generally think of events like assassinations as "scientific" facts, but the murder of President Kennedy is as fully corroborated a fact as can be found anywhere, and it would betray a profoundly unscientific frame of mind to deny that it occurred. I think "science," therefore, should be considered a specialized branch of a larger effort to form true beliefs about events in our world.
So, there is science as "broadly construed", which is our best effort to form a rational account of empirical reality, and there is science as "a specialized branch" of that effort. That seems fair enough to me.
We just need to be clear what we're talking about in a given context. E.g., if I ask a friend what she's studying at university, and she says "science", I'll assume with some confidence that she's referring to stuff she's doing in the science faculty - she's probably not, for example, majoring in French literature or in constitutional law. She's doing stuff that falls in the "specialized branch" that Harris refers to (and there's other perfectly good stuff she could be doing which doesn't fall there). In most contexts when we talk about science, this is what we have in mind, and there are historical, pedagogical, etc., reasons for that.
But science in the sense of the specialized branch isn't radically discontinuous from everything else. Though we can point to it as something specialized, we also have to acknowledge that there's no "hard distinction" between it and the rest of rational inquiry. Or as I'd put it, science (the specialised branch of inquiry) is continuous with other branches of rational inquiry.
I think that Harris is pretty much correct on these points. Doubtless y'all can think of some additional subtleties, but Harris seems to get things about right, at least in this quote.