dealers often 'buy' a warranty anyway. Theses most often dont cover cam belts, and even if they did many would only cover the part that broke, and not 'secondary damage'. So literally just the belt.
I brought a warranty for a second hand car a few years ago, who were about double the cost of others. This company explained why they cost more and even used a broken cambelt as an example. They included the belt and secondary damage. I checked the other companies at the time and they confirmed that they would either not cover it at all, or just the cost of the belt!
I dont think you have much chance here at all. The only thing would be if it was sold and the cambelt was overdue a change. The engine as you state was changed at 40,000 miles, was this a new engine? can it be confirmed it was changed? can it be confirmed that it had a new belt and not the old one?