More times than not, the sponsor will automatically readjust the value down. All of our trips ended up costing less than half of the ARV. On two occasions, we had to request the sponsor readjust the 1099 down which they did. It sometimes is an oversight when they fail to give Accounting the proper paperwork on the trip.
However, there is always a chance a sponsor will refuse to readjust the value.
So, you need to document everything that the sponsor is paying for on your trip. As soon as you get your itinerary look up the prices for the exact flight and seating costs and also the hotel costs. Find the lowest price on the internet you can and print it up. During your trip don't be afraid to ask what the extras cost that the sponsor is covering. We had to call up the limo service that took us to and from New York to get their fees for that. Get as much as you can on paper and write down anything else. When everything is done and over, add it up and put it away for tax time. When you get your 1099, see if it matches up. It may actually be lower, because sponsors can sometimes get lower special rates on such things as hotels.
If the figure on the 1099 is the ARV or way off from your totals, request that they change it. If they refuse, just submit the figure you have.
The IRS says not to send in the documentation with your tax return but to keep it filed away with a copy of your tax return in case of an audit, but some people do choose to send along the documentation.
The IRS requires that you pay taxes on the fair market value (FMV, true value) of the prize, not the ARV; and this is stated on their site.