White light contains light of all frequencies, so a violet paint that only reflected a single frequency would look very dark since it would only be reflecting a tiny proportion of the light that hit it. Even if it reflected a range of frequencies around violet it would still look very dark unless the range was large enough to also contain a lot of blue.
If you wanted to see "true" violet, your best bet would be to find a monochromatic violet light source. A Blu-ray laser would do the trick. But it won't look any different from the RGB imitation aside from being brighter.
EDIT: Please do not shine a Blu-ray laser directly into your eye.
How about a blacklight? The frequency of light you can see leaking through the filter is 404nm, so that should be a relatively safe way to see what "spectral violet" looks like, right?
If your white light source has a flat spectrum, then the violet paint wouldn't be any dimmer than any other color. The reason red or blue paint looks bright enough to see is because, as you said, they do reflect a range. So the violet paint could reflect the same bandwidth range as the traditional visible spectrum paints, and it would have the same power density.
Unless you mean appearance, in which case, yeah, our eyes don't detect violet very well.
If you wanted to see "true" violet, your best bet would be to find a monochromatic violet light source. A Blu-ray laser would do the trick. But it won't look any different from the RGB imitation aside from being brighter.
EDIT: Please do not shine a Blu-ray laser directly into your eye.