Well, you are confusing scales and keys, two different things - as is that wikipedia quote - but the point that the key of C major's "relative minor" key, in classical lingo, A minor, with the same key signature, uses the Aeolian, since A to A using the C major notes is Aeolian, is a good one, thanks.

[looks at the page] Wow, the scale of "A minor" has a wikipedia page?!..uh no, it seems it's about the key of A minor, and the whole thing confuses the key and the associated scale. That's very weird!

To explain slightly - in my understanding, saying a classical piece is "In C minor" as they do, usually means it starts and ends (at least) in the key of C minor. "C" means the root or I of the home/tonic chord is C, "minor" means the third is Eb ("major" would mean it's E). The fifth is always G, so not specified. This key specifies the (most important/initial) root triad. It says nothing about the other notes of the scale. The most important chord besides the I chord, the V7, has a B natural, which will usually occur often in the melody, and is not in the "natural minor" scale. Etc. Key =/= scale.