I am installing CiviCRM in Amazon AWS environment. User civicrm has full rights on civicrm database. I certainly see TRIGGER among all others in my phpMyAdmin console. Out of abundance of caution I even gave global TRIGGER permission. Still, I am getting the error. I had a test installation with DB running on the same server as web server and didn't have any problems. Don't know if CiviCRM doesn't see TRIGGER permission because of different host, or because of RDS limitations, or yet something else.
Web Server is Amazon Linux (similar to Fedora/CentOS); Apache 2.4; MySQL is 5.6.27
UPDATE: I tried "root" account and I get the same error. I don't think (or at least I don't know how) I can spool the SQLs that get generated - so if somebody can point me to a query that tries to create a trigger and fails, that would be awesome!