Another data point. I just cancelled an online booking I made yesterday over the phone. Booked an American Airlines flight. Online, clicking on the "Cancellation Options" indicated that I could not cancel online. Had looked around the web and it was suggested that within 24 hours of making the booking, you could receive a full refund for a cancellation. So far, this appears to be the case for me. Avios were back in my account immediately. Agent indicated the $5 refund (it was two one-way tickets) would come back in 8-10 days. No charges for using the phone, and certainly no extra charges for cancelling.