Not wanting to start a war, but few airlines treat their ultra-exclusive Arrivals Lounges the same way as their general club lounges, and so "is" is "not always". Given Dorian's past experiences, you were being very gutsy KH, and I am sure you never expected being let in. While you are technically correct, such lounges are intended for overseas overnight travellers in J-class (and Y-class SEs and ExecPlats?). You'd have gotten the same reception in the past at BA's Arrivals Lounge at T4, even though oneworld emerald and sapphires technically have lounge privileges, these remain off-limits.
It's like I noted in a recent email to EMPRESS, the airlines still operate a class/ caste system, and discrimination in the air (and on the ground) is still a fact of life based on who can pay. Upgradeselite members don't necessarily get all the perks. I suspect the same operates with AA's new international F-Class lounges.
I'm not saying this is "right", but this is how it is.