You may need the "physical piece of plastic" if you're flying on a oneWorld partner airline, since their computers and boarding passes don't always show AA status. If you plan to do that, take evidence such as a recent statement, a printout of your View Miles page from the AA Web site, or a recent AA boarding pass. Their staff have no other way to verify your claim. They may, understandably, be a tad skeptical of "I didn't get my card yet."