If I type 0 on Blockcypher, it will return a error:
Server Error (500)
It is usually interpreted as block zero yes. It's just a matter of how these sites index/display it. It looks like Blockcypher is indeed reffering to both the Genesis and the normal first block as Block #1, which indeed looks a bit weird. ( And i doubt that it is done intentionally...)
A better way would indeed be to display it like this,
Block #0 https://blockchain.info/block-index/14849/000000000019d6689c085ae165831e934ff763ae46a2a6c172b3f1b60a8ce26f
vs
Block #1 https://blockchain.info/block-index/14850/00000000839a8e6886ab5951d76f411475428afc90947ee320161bbf18eb6048
Also,