Zerocoin.org is not run by Zcoin. Zerocoin.org is owned by Ian Miers (imiers) who is one of the founders of Zcash and also worked on the Zerocoin whitepaper. You can see this clearly in the footer of the website and his link to Zerocash.

Zcoin is built using the Zerocoin whitepaper but there's no 'counterfeiting'. There is no claim that Zcoin devs came up with Zerocoin, they claim correctly that they are the first to implement it. There are two papers here, Zerocoin and Zerocash which expands on Zerocoin.