Don't believe they promise you transportation on a specific day. I think they promise you transportation, and by offering you a refund, they are allowing you the option to cancel.
I just had US Air do this, they canceled a flight I am on in May, they didn't tell me I noticed the itineary was messed up, and their only offer was a refund or fly the day before. I asked about putting me on another airline, they laughed. They repeated I had the option of a full refund if I didn't want the earlier day.
I should have played dumb, I should have flown down and pretended I didn't know it so they would put me on another airline, but with my luck I would be stuck for days waiting for a seat.
If they didn't offer you a refund, then maybe you had a case, but as long as the refund is offered, they are probably covered on their end of the carriage.