The OP made a rookie mistake: Not researching the peculiarities of a tiny one-horse town's airport before assuming they were departing LGA. The contract US Express agents did nothing wrong. As is often the case, this one is on the traveler.
From the aa.com page on New Bern, NC:
New Bern, NC (EWN)
Special notice
Check in three hours before departure. Security checkpoints close one hour before departure.
http://www.aa.com/i18n/travelInforma...wn-airport.jsp
There's a link to the airport website from that page, and the airport website says:
Please arrive 1 hour and 15 minutes prior to your departure time.
http://www.newbernairport.com/
It's one thing to cut it close when time is so valuable; it's quite another to complain without any basis to do so when you cut it too close and get burned.
OP: Like many other mistakes, this is a learning opportunity.