Yes exactly. Look up the Nano ledger X for example. I look at it like money in the bank. Does the bank really have all our funds if we went to withdrawal? No they don't and God knows what they do with it all. There was a thread last year on the increasing number of large BTC wallets that were pulling their bags off the exchanges to cold storage which tells us all we need to know.

Unfortunately the whole crypto space is confusing and even more confusing/time consuming when you use cold storage. Most will just leave their funds on Coinbase etc... and think their money is safe.