Yeah that's the conventional dose rate effect, not the FLASH effect. The FLASH effect happens on timescales so short that ordinary considerations like the cell cycle or DNA repair mechanisms are inherently ruled out. Instead it might have to do with the type of radical species that form in normal cells versus tumors, possibly related to oxygenation, pH, glycolysis byproducts, etc.
The first interaction of radiation with tissue is usually this:
H2O + ħv >> H2O+ + e- (fugitive)
The radical ion H2O+ is extremely reactive and usually protonates another water molecule immediately:
H2O+ + H2O >> H3O+ + OH*
The hydroxyl radical has a half life of about a nanosecond and will usually be the main "reagent", diffusing until it runs into an organic molecule which will be oxidized and thus degraded. At high enough dose rates, the peak concentration of hydroxyl radicals and more stable radicals like superoxide could be much higher, leading to "nonlinear" effects, i.e. byproducts of multiple radicals interacting with each other or a protein.
One thing I found confusing about the nature article is that it mostly discusses conventional linear accelerator + bremsstrahlung X-ray radiation versus very high dose rate FLASH in the form of electron beams, proton beams, or even carbon ion beams.
Do we know that what the chemical mechanism for damage from charged particle beams is? Is it similar enough to compare directly like this? Are the timescales short enough that charge deposition might matter?
The article is a bit unclear, but we have both a very wide range of X-ray vs charged particle studies, and increasingly of conventional vs FLASH studies with a range of modalities (e.g. the seminal FLASH paper was FLASH electrons vs conventional electrons). FLASH photon vs conventional photons are also increasingly being generated, although they've been more of a pain to generate.
So it's clear there is a temporal FLASH effect, which is not purely a question of radiation type.
That's not to say it's necessarily exactly the same effect - we still don't have a perfect quantitative understanding of the effects of different radiation types even at normal dose rates, let alone when FLASH differences are added into the mix.
For the other readers in this thread, this poster really knows their stuff.