I don't think a separate policy is a requirement. The AA citi exec is just bad. I believe Chase's cards for example do not impose a 6 hour delay on the offending segment, they just require the overall delay was 6 hours (or overnight.)

This was one of the "benefits" rolled out and marketed when the annual fee increased which in practice has very limited utility.
These insurances are most useful for connections IMO and necessitating a 6 hour connection for the protection to apply is ridiculous. AA doesn't even allow 6 hour connections on domestic revenue tickets without a broken fare lol.