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)
but why on reddit they are implying otherwise? i find it strange that you have only one day windows for the claiming, it make more sense if there was a range of days, well i think i'm going to throw a wallet at it and see what i can get