From my experience, having the load you are towing weigh less than the vehicle which is doing the towing is a very good start. The camper would have it's own brakes to be legal I am guessing, are they manual or electric?
On a camping trip to Europe 6 years ago I was amazed at the amount of what we consider in Australia to be small cars towing these Euro light weigh full on caravans. It was not unusual to see VW Golfs with small vans on the back.
So I recon you can trust in the number Toyota is quoting, and as always when towing, drive with much more caution, as physics works against you when you double your mass with a trailer on the back.