The hypothesis that a balloon filled with water will be able to withstand fire is proven to be true.
Most of the balloons are made from rubber which has a thermal conductivity of 0.16 W•K-1•m-1. The yellow colored balloon was filled with only air which has a thermal conductivity of 0.025W•K-1•m-1. Therefore the balloon surface over the candle was not able to transfer much heat to the air inside the balloon. The rubber surface became hot, melted and the balloon exploded.
The blue colored balloon had water and air inside it. Water has a thermal conductivity of 0.6 W•K-1•m-1 .The water was able to absorb the heat on the balloon surface when it was held over the candle. The temperature of the balloon surface was kept low and it did not explode.
Try a different experiment by placing the inflated balloon in hot water and cold water to observe the changes.
Thermal conductivity - http://en.wikipedia.org/wiki/Thermal_conductivity
What is thermal conduction? -http://www.wisegeek.com/what-is-thermal-conduction.htm