The above statement which you quoted is from block.one. They do not have any intention of generating a genesis block and standing up a blockchain. However, they are freely giving the EOSIO software which they are developing to the community and the community will stand-up a blockchain. At least that's the hope. And it's certainly reasonable since a lot of people have a vested interest in seeing an EOS blockchain up and running -- not just hodlers, but Dapp developers as well.
In order to generate the genesis file, the Ethereum blockchain will be queried for all addresses that are holding EOS tokens and have registered them with the EOSCrowdsale contract. Those EOS tokens will become EOS tokens (coins?) on the new public EOS blockchain. For more about registering your ERC-20 tokens: https://steemit.com/eos/@sandwich/contributing-to-eos-token-sale-with-myetherwallet-and-contract-inner-workings
RE: EOS Announcement Indicates They Will NOT Be Their Own Blockchain