This isn't true (at least in theory). Octaves on piano are (or should be) exact, otherwise the 12-tone equal tempering doesn't work out. A4 is 440 Hz, A5 is 880 Hz, and A3 is 220 Hz (using the Acoustical Society of America designations, where middle C = C4). If the octaves weren't pure, the piano would be more in tune in the middle than it would be at either end, which usually isn't the case.
> There were experiments with more tones per octave back in the middle ages, but the idea never caught on because the musical benefits aren't obvious.
The history of scales and how they came to be in the Western classical system is long and complicated (too long for here, certainly), but I wanted to point out my favorite of these weird old instruments the archicembalo.[1] It was designed by one of the most out there theorists, Nicola Vicentino, in Ferrara, a hotbed of weird music at the time (see Carlo Gesualdo's "Moro lasso" [2], a really chromatic madrigal).
1. http://en.wikipedia.org/wiki/Archicembalo 2. http://www.youtube.com/watch?v=s_q3EJNUKis
(I'm ABD on a Music Theory PhD, so if anybody has more specific questions I'm happy to help!)