– that is absolutely correct. Have a look at the spectra I posted here - you clearly can see the rather sharp peak of a blue LED plus the additional broad peak of the photoluminescent dye creating the impression of a “white” LED. Depending on the material parameters, nowadays you can get rather flat spectra afterall (see the spectrum 5000K posted by @PM490 just above my post). So nowadays, you do get white-light LEDs which have decent flat spectrum.
Actually, I think one topic is often overlooked when discussing LED illumination with respect to scanning color reversal film. First, no every white “LED” is created equal (see above). Than, even a perfectly flat spectrum will no correspondent to the spectrum of the projection lamp used to view the film in the old days - neither a halogen or xenon lamp does have a flat spectrum.
Now, the topic I would like to discuss is the following: film dyes were designed with a certain light source in mind - within that setting, a very good color balance throughout the full color space was obtained. However, using a light source with a different spectrum will introduce subtle color shifts within certain color ranges, depending on the spectral filter properties of the film’s dyes.
Well, from a signal-processing point of view, that should not really matter too much - you can adjust all of this in post production, provided you work with a sufficient bit depth along your signal path.
However, if you do not use a broad-spectrum LED setup, but a LED-source composed of single red, green and blue LEDs, you do end up with a spectrum composed of three rather narrow peaks. If these peaks are perfectly matched to the dyes of the film and the filter curves of your scanning camera, you will be rewarded with a great color definition (in terms of saturation mainly). But: what will work well for one film stock will not work that well for another one, at least in my experience. I am using for scanning a light source of different red, green and blue LEDs, mixed together in an integrating sphere. The Super-8 material I am scanning shows noticable variations in terms of color definition. While this is expected for different film stock (like Kodak or Agfa material), you notice even within a single film variations at that point in time when the material came from a different 15m-cassette. I think that effect is related to the difference of scanning a film at three well-defined spectral peaks (combination of red, green and blue LED) versus scanning the film with a broad spectrum (white LED, sampling over a larger spectral range for each color channel).