Haha! They said they don't know what iCloud account is was registered under. Everything in Apple's world flows from the iCloud, so even with the receipt, the first thing they'll ask is to login and confirm the account is on your iCloud account.
I hate being held hostage to a corporation. Anti-theft mechanisms propagated from a corporation should be understood to generally benefit the corporation first (monopoly on resale market) and the user second (limited protection from petty theft).
I know I'm charmed to live in a place where petty crime is relatively low, but these sorts of "lock it to my Apple account" anti-theft tools feel awfully similar to the use of martial law. It's very helpful in limited circumstances but should never be the default state of our lives.
https://al-support.apple.com/#/getsupport