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It is weird that you don't see any records on coinbase. Did you maybe use another account? Or a different exchange?
You are right bob, all the bitcoin services (exchanges or casinos) have a record of all the deposits, transactions, and withdrawals.
OP could verify directly in the blockchain that information only if he has made a withdraw to a bitcoin address anytime he made the purchase. If he only keeps the bitcoins in the exchange then it will be impossible to verify it from the blockchain.