It may be that by entering your EA info, the website automatically defaulted to the EA contract ID, which isn't always the best one to use.
I log into National first with my EA info, then I put in the
AAA code found on Mousesavers and any relevant coupons or specials. That's how I usually get the best rate. Sometimes other Contract IDs are as good as EA, but I haven't found a better combination for my needs yet.
I wouldn't show up to the EA, choose a car, and depart unless my confirmation specifically statd EA. I booked once through the AAA website, but the confirmation didn't state the EA info (and I couldn't enter it anywhere on the AAA site). I emailed National, and they were clear that ressie didn't qualify for EA service. Fortunately, they canceled the ressie and rebooked at as an EA ressie at the same price.
Dirk