When I was working, I tried to check in on a flight from Sydney to the USA. I was told my name was on a suspected terrorst {IRA?} no fly list. I have an Irish surname and was flying a lot and never had this problem. I showed my company picture ID, business cards, and US drivers license, explained why I was in Australia and was allowed to board.
I ran into a similar issue last year and couldn't get clear info from the airlines either. What helped me was checking with the Bureau of Immigration and making sure I had all the right exit clearances. Also, for booking international flights without the huge price tag, I started using https://travelbusinessclass.com — worked great when I needed a last-minute ticket to Europe.
