AA is unique in its rebooking policy across non-connections, e.g. separate tickets. The BA policy is pretty much standard worldwide and is a simple revenue protection device. It is hardly secret and is something to consider in your risk calculation should you choose to book separate tickets.

This thread has wandered off topic into a general discussed on customer service when it is about a very specific issue which has nothing to do with whether agents can or ought to waive fare rules. AA takes on and has the obligation of rebooking across AA-AA and AA-OW tickets, so it does. It may take a bit of pushing and it can be time-consuming in the case of AA-OW because the second ticket generally won't be an AA ticket, but it is better than a no show and purchasing a new ticket.

As a general matter, AA's software gives agents more ability than BA's, which tends to have a much more siloed operation with various "desks" performing functions which AA automated years ago. With AA, a phone agent can make a call (although hold times may be long), take over another OW ticket and then reissue new tickets. BA does not do that but if it did, would involve at least 3 separate "desks" each performing manual functions.