I don't know why the particular block heights were chosen. I didn't hear about CLAM until a while after it launched.
The specific blocks at which the snapshots were taken:
BTC block 300377 (2014-05-12 12:48:17)
LTC block 565693 (2014-05-12 13:06:31)
DOGE block 218556 (2014-05-12 13:09:17)