There's almost every horticultural website delivering false information in an attempt to sway a potential buyer to their own brands, with one of these arguments is by spectrum talk, either "we have FR for Emerson" or "we have no green as chl doesn't absorb that" [sic!] or whatever.... The problem isn't the spectrum but the advertising....
I'm not really sure to what SPDs or lamps you refer when stating they did so without the benefit of FRL? As all HIDs contain quite an effective dosage of FRL and even white LED have something like 3-5% on board, it depends a bit on CRI and K temp. One would have to use a "NASA" light made out of solely monochromatics to not have FRL in the SPD.
Now when I write FRL is very effective then this could mean a number of things, one is the selectively excitation of photosystem I (PSI) that starts when the absorption of PSII sharply declines at around 680nm, which is where its funnels core (p860) has its max-absorption peak. Still, a bit of FRL is absorbed by PSII, but only about 1 out of 10 photons, the rest is increasingly absorbed by PSI.
Now this is much of a greater difference as the ratio of PSII:PSI absorbance in the PAR region. Thus, FRL is very effective to do away with the exciton overflow happening at the binding site where PSII hands over electrons to PSI.
You can see this here:
View attachment 1337793
^^ for a leaf (it really doesn't matter if it's lettuce as chloroplasts/photosystems are similar for all plant species), what's important is the reduced fluorescence when FRL is introduced, as that is a very strong indicator of a better photochemistry (less exciton loss via fluorescence),
or here:
View attachment 1337795
Which shows the famous "Emerson-enhancement effect" on a sunflower leaf,
or here:
View attachment 1337796
Which shows net canopy carbon gain in a rigorous approach with or w/o supplemented farred light, and very interestingly, the small arrows also show the decrease in photosynthesisrate when the supplemented FRL was dropped shortly. Now this very drop is bigger in the "RB+FRL" setup than in the "White+FRL" setup - because Bugbee used a warmwhite 3000k spectrum for this, which contained already (IIRC) 5% FRL (the RB next to none).
In other words, we can even discriminate between the longterm effects of FRL on the habitus of a given plant (also including bigger leaf-size from the phytochrome effect) against its immediate effect on the photosynthesis rate.
But there are many ways to illustrate effects of light and it is true that it is only PAR light 400-700nm that is crucially needed for plants to acquire mass. If FRL lacks, then one antenna of PSII can wander to support PSI with excitons to due away with this overflow (you see this also evident in the first 2 pics where the fluorescence slowly drops).