:As I read the article, it is asserting exactly what you are asserting: the two example sentences are indeed illustrating the same thing. The point the article makes is that different names are used: popular language calls this thing "singular they", linguists call it "plural anaphoric they". Sure, it's the same thing.
I'm not sure where you get the idea of indeterminate number "shifting" to indeterminate gender. I, for one, agree with you, there is no such "shift" in English (unless it lies a long way back in the history of English pronouns, but that's another, and long, story). The article, however, at least as I read it, also agrees with us. It asserts there are two types of indeterminacy, either or both of which can be marked by use of they. Where does it say one "shifts" into the other?
Regarding your sentences, you have constructed them such that all have indeterminate gender. The first, however, could clearly apply to 0, 1 or >=2 people, so also has indeterminate number (or is plural, per Givón). The key thing is that all your sentences involve universal quantification over the domain (or restriction) of a variable: for all people or students x in X, your sentences assert something that is true for person or student x. Because there is a plurality of x in X, Givón and other liguists, call usage of they, in constructions such as yours, plural. Because each x is a singular person (in the first sentence a hypothetical person), ordinary people, like you and me, call this usage "singular". In fact, though, these constructions are distributive (one assertion to each of many people), which is why grammatical number cannot be well defined. There is no specific reference, so singularity or plurality can't be derived from a referent in the usual way. The constructions have either generic reference, or no reference at all.