I will go out on a ledge and suggest that this
http://www.billtroxler.com/f/25_Aeolian_Mode.pdf is what you are referring to. It is wrong.
1) Things I agree with in this document
Every scale has characteristic chords and notes - simple result of having a tendency for some notes that want to rise or fall.
C major (C Ionian) tones are C, F and B: F has a tendency to fall to e, B has a tendency to rise to C; chords are C, F and G - between them , they contain all of the notes of the scale.
2) Things I disagree with in this document
You do not build a minor chord above mode tone [sup]b[/sup]6 - that would be F minor in A aeolian (F-A[sup]b[/sup]-C) which contains a non mode tone A[sup]b[/sup]/G[sup]#[/sup] - no method for constructing the Aeolian that I can think of allows this particular construction (you might get away with it in the harmonic minor by fudging the use of the raised 7th and pretending it is a flat 1 instead
3) Why I disagree
In A natural minor (A aeolian) I would have thought that tones were A B and F and the chords were Am, Dm and G (again all notes of the scale appear in these three chords which is not true if you use F instead). Note that by using B and F as the other significant tones in the scale to construct a chord, we end up with Bdim (B-D-F) and G[sup]7[/sup] (G-B-D-F) as possible significant chords, further reinforcing the idea that G is the natural 3rd chord in the triumvirate of significant chords (yes we could have used Em, but it is not as solid a cadential force as G as in Em-Am vs G-Am; the second construction sounds more final and is in fact known as the Aeolian cadence).
In spite of many remonstrations against relying solely on wikipedia for some aspects of music theory,
this article serves to provide a better overview as does
this website