I am a student working on a doctorate in geochemical volcanology and I can tell you that explosivity can be caused by water but that is not the reason that basalt is not explosive. The explosivity can be found to be dictated by the make up of the melt. The more silicon in the melt the more viscous it is, this means that silicic lava called rhyolite can bind up much more gas than basalt and therefore contains far more pressure to be erupted when the melt can no longer hold the gas. As far as I know all lavas need water and other volatile gasses to form because it lowers the melting point and dissolves the rock.

When a magma source encounters a body of water it creates a large explosion called a phreatic eruption. These kind of eruptions can occur at any volcano with a water source above it or around it and are usually very violent eruptions.

The next time Yellowstone erupts there will most likely be a phreatic eruption in the early phases of its activity because of the massive Yellowstone Lake that sits atop part of the calderas rim. With Yellowstone obviously this would be a small matter in the heat of a super-eruption event.