What they actually showed is that 1) much of the current does not reach the brain, and 2) the current that does is not sufficient to directly “force” neurons to fire. However, that doesn’t mean the remaining current does nothing at all, as it could still modulate brain activity.
Using direct recordings of individual neurons, I showed that various forms of tES shift spike timing. Simulation causes them to fire sooner or later than they otherwise would. This matters because information is carried in both by overall rate of spiking and the timing of those spikes. Moreover, it’s not just a placebo, because knocking out the sensations with topical anesthetic doesn’t block the neural effects, nor is recreating them sufficient to cause them.
I just wrote a little think-piece about this for PLOS Biology that summarizes what we know—-and don’t—-about it
https://journals.plos.org/plosbiology/article?id=10.1371/jou...