Which does not mention any effect on open brood present at the time of trickling or spraying. The relevant result is:
"The amount of brood after four months is also of interest. In particular, sublimation resulted in significantly more brood than controls, at 4.8 (average of the four treatment means) vs. 4.1 frames. The numbers of frames of brood was not different among control, trickling, and spraying colonies. However, there was a trend towards lower amounts of brood with higher doses for both trickling and spraying. Previous research also reported a negative effect on brood rearing following the application of OA via spraying and trickling (Higes et al., 1999; Rademacher & Harz, 2006)."
So the amount of brood present 4 months after treatment.
Higes et al (cited) took a similar measurement, that being that there were 8 weeks of "kill and count the surviving mites" using Fluvalinate and then (because they had resistant mites) coumaphos. They they looked at how much brood was in the colonies 8 weeks after the final OA application. They found a statistically significant reduction in brood levels compared to control (which in their case was water spraying).
Rademacher & Harz (cited) didn't actually conduct any experiments for that paper, they reviewed previous work. Within that review they tabulated "brood cells present" where original authors had provided that data - there is no detail given by Rademacher and Harz as to whether previous author's techniques were comparable which is not really surprising given that they don't make any conclusions relating to the effect of treatments on brood, only the effectiveness against mites. It appears to be a bit of a false reference.
So Toufaila, Scandian and Ratneiks found that 4 months after treatment (brood lasts 21 days) there was the same amount of brood in untreated controls, trickling, and spraying, but statistically significant more in vaporised. That sounds good, healthy colonies rear more brood, I think most people accept that vaporising OA does not negatively impact the bees etc., but once again, this doesn't suggest any negative impact on the open brood.
I suspect it may be this result - misunderstood or misquoted - and perhaps others like it that are becoming the "story" about trickling killing open brood. If it is not, I hope we stumble across whatever result which does show harm to brood, but in the meantime I will remain sceptical on the basis that I've not seen data and that the cited sources show something different to "harm to brood".
In practical terms all of these results still support both delivery mechanisms, and seem to slightly favour vaporisation.