There are absolutely ways to deal with what you call interconnected data, as I mentioned earlier: paired tests, corrections for autocorrelation, nonparametric and bootstrap methods for non-normal data and so on. But barring any examples of what you mean with interconnectedness in this context, it's hard to recommend any studies or publications because there is no One Method Of Interconnectedness Correction.

Also, statistics deals with many idealizations but the idea that randomization allows you to cleanly measure the effect of an intervention in the face of what would otherwise be confounding is simply not one of them. Sorry to disappoint, but with all you're telling us it simply sounds like the speaker was clueless.