How does boiling water release dyes from vegetables?
Why boiling water releases dyes from vegetables:


In general, one would need a solvent to extract compounds from the vegetables. Water is a solvent for the coloured pigments. In air or oil, the same pigments are less or even not at all soluble.
Hot water can damage cells. Proteins, which give structure to cells and membranes, denature at hot temperatures. Cell walls, by the way, are much more robust than membranes.
But even in cold water, some pigments can pass through membranes or membrane channels by diffusion. This will only take more time.


There are possibly other factors that are more case (vegetable) specific.