You missed the part where there are no "actual" bitcoins. All that exists are transactions that are stored in a blockchain.
If you create a new blockchain, then it will have it's own transactions. Those transactions won't exist in the bitcoin blockchain (and vice-versa). Therefore, they won't be "bitcoins" , they'll just be alt-coins that have the same protocol rules as bitcoin.
There won't be a way to send a transaction from your blockchain to the bitcoin blockchain, since in order to be valid EVERY bitcoin transaction must contain a reference to previous unspent transaction outputs elsewhere in the bitcoin blockchain.