In normal circumstances (say, daylight surroundings), a moderate amount of light at very short wavelengths won’t look like much of anything at all, bluish–black, because the cone cells (especially L and M cones which determine red–green response) will be getting much more stimulus from other wavelengths.

If you go to a completely dark room, let your eyes adapt, and look at a blacklight, then you are right that you are at that point going to see it looking purplish because the L cones are stimulated a bit more than the M cones for those wavelengths, and other wavelengths are entirely absent. But this is a really weird edge case for vision.