Recently I created an account/wallet on coinbase.com. Then I transferred my BTCs I already had from blockchain.info to the wallet on Coinbase.
A bit later I bought some new bitcoins directly from Coinbase with my credit card and I expected that I'm able to see something like a transaction ID and a block reference once the new BTCs arrived in my wallet.
Interestingly I got the BTCs but there's no transaction of block reference as expected.
On support.coinbase.com they say:
You can view most digital currency transactions on the network's respective blockchain, which records and verifies the legitimacy of transactions. However, when transferring from a Coinbase account to another Coinbase account, the transactions occur off the blockchain. […] For these "off-chain" transactions, you won't be able to view the bitcoin transfer in the blockchain, and there won't be an "Advanced Details" link when you click on the transaction.
As far as I understand the bitcoin blockchain the idea behind the whole thing is that everybody knows how many bitcoins I own (yes I know, my identity are hash addresses).
But if there's something like off-chain transactions this means that I don't own the BTCs I bought with my credit card, from a technical point of view because no one (the distributed ledger) know's about this transaction.
Is this correct?