Most non-phosphor type LEDs DO have a "dominant" wavelength (some are very "pure" and do emit in a single one), but we should not confuse that with being the "color" of the light emitted.
I think the mushroom piece is incorrectly interpreting things. If you read the wiki article on Wein's law, it says the
predominate wavelength can be predicted, but that does not tell you anything about the appearance of the light. Examples given includes the sun (5778°K) which calculates out to a predominate peak at 502 nm - right in the middle of the visible spectrum - and an incandescent bulb (1500°K) being 2000 nm, which is WAAAY in the infrared. If we took that to represent "the" wavelength that interacted with our plants, we would incorrectly conclude that an incandescent bulb can be of no value, as that 2000 nm does not correspond to any absorption by chlorophyll.
Earlier, it was mentioned that 644, 707, and 828 nm were the "dominant" color emitted by lamps of 3500°, 4100°, and 4500°K. Maybe I am TOTALLY missing something - and I have read the Wikipedia article to which we were referred by the mushroom site - but I still cannot buy the "color temperature relating to a single wavelength" assessment because none of those wavelengths correspond to white light at all - 644 nm is very red, while 707, and 828 nm are both in the infrared.
If you look at the spectra corresponding to those color temps (below), the peaks are, indeed, at the wavelengths the calculation would predict. But you can see that they do represent two IR and one red light, while the color we would see - due to the other wavelengths in the spectrum) are yellowish to bright white represented by the "appearance" dots associated with each.
There are a couple of other things to keep in mind:
1) Chlorophyll absorbs in the blue end of the spectrum too, and none of those light sources is particularly strong in the blue end.
2) Shifting to the "hotter" light gives you significantly more intensity of light in both of the chlorophyll absorption regions - including those tree specific wavelengths in the red/IR end.