To add to the confusion, AA distinguishes between their standby policy (standby permitted by fare rules and/or elite status) and Same-Day Standby ($75 product sold to passengers who are otherwise ineligible for standby).
I think you would have been permitted to standby for free on the domestic portion per the standby policy, but your girlfriend would not have been permitted to standby as your companion because you were on separate records, and she could not have purchased the $75 Same-Day Standby product because it was part of an international itinerary. But then again, premium cabin tickets are permitted by the fare rules to standby for free on domestic flights regardless of status, so... I have no idea, to be honest. Just throwing some more information out there.