Can't launch any version of Minecraft if game directory is changed

I created a new profile in order to play in an older version of Minecraft and found that I couldn't launch any version from alpha to 1.7.4 (current).

All I did was change the game directory in the profile settings to <default path>/minecraft-alpha and select an older version from the dropdown list.

What happens:

Alpha - black screen
Beta - blank screen
recent versions - nothing (application icon appears in dock but no window appears)

Additionally, I saw that it downloaded the older versions to <default path>/<default game directory> and that <default path>/minecraft-alpha contained only logs/latest.log and output-client.log.