In the future, you should always check with the Dept. of State for the most up to date advice regarding entry requirements for US citizens. The best source, in my opinion, is the Dept. of State Consular Information Sheet for the country concerned. See http://travel.state.gov/travel/cis_p.../cis_1093.html
where it clearly states that:

"For entry into the country, Costa Rican authorities require that U.S. citizens present valid passports that will not expire for at least thirty days after arrival."

I believe this is a new requirement (a birth certificate used to suffice), and indeed the Consular Information Sheet reflects at the bottom that it was updated on October 13, 2005 to reflect changes to Entry & Exit Requirements, among other sections. So, depending on when you inquired with AA, you may have actually received correct advice at THAT time. It's a shame that Costa Rican immigration didn't make an exception, but certainly not AA's fault.