You are (typically) being checked by an airline staffer for the simple reason that if they fly you somewhere where you are denied entry, they may be obligated to fly you back on their next flight. It's a fair bit of behind-covering for the carrier, but doesn't have the authority of the inbound country's border controls.

(I also have my passport on file with Delta. It's rare that my passport is checked carefully before boarding an outbound flight to Europe.)