Glad to hear this didn't totally wreck your plans and that you've re-booked your travel on another airline. We're fortunate in Phoenix to have many choices for both domestic and international air travel and because we're a "hub" city for two major airlines fares are pretty competitive across the board. I shudder to think what might happen to Phoenix Sky Harbor and the Valley's economy if US Airways was to go belly-up.
I hope CheapTickets does the right thing and refunds your money. They lied when they told you to expect a refund directly from AirOne/Alitalia. When you paid CheapTickets your money did eventually go to AirOne but through the agency. Since they are the agent they should initiate the refund request. AirOne should refund ChepTickets through their IATA settlement account and then CheapTickets should, in turn, refund the money back to your credit card. Of course disputing through your credit card can't hurt and will likely expedite things.
As for your insurance that's just downright absurd. I've heard some stories about Access America and this sounds just like something they would pull. I had a friend who cut his vacation short a couple of years ago because he pulled a muscle in his neck and shoulder and wanted to return home to see his chiropractor. He paid the change fees, etc. and filed a claim with all of the documentation the insurance company required. He actually saw the Chiropractor the afternoon he arrived home and faxed everything from the doctor's office. His claim was denied because he had been seeing his Chiropractor off and on for several years and they deemed his injury a pre-exisitng condition based solely on that fact!
I posted in this thread about
another travel insurance company which seems to offer more comprehensive coverage including coverage for loss of or change to employment. You might want to check them out before taking your trip.