If you add dye to a shirt the situation gets more complicated. Dyes strongly absorb certain colors and strongly reflect other colors. However, the surface of each individual dyed fiber still reflects a little bit of all of the colors. This means that a dry blue shirt is actually whitish blue (which we call "lighter blue"), but the same shirt when wet is just blue (which we call "darker blue"). Adding water to a dyed fabric inhibits the multiple reflections, so more of the light has a chance to be absorbed by the dyes. Therefore, adding water to a heavily dyed shirt does not make it more transparent. It makes the shirt have a darker, more saturated color.