The band of biologists who redrew the tree of life

In a way, yes. It’s widely established that 20th century biologists got to pick the low-hanging fruits. This shouldn’t detract from the sheer genius they displayed.

In the specific case of the three domains of life (bacteria, archaea and eukaryotes) — which I’m assuming you’re referring to? — Woese & al. got “lucky” with their study of 16S rRNAs.

In a nutshell, these RNAs are relatively easy to sequence and analyse. Their extremely high degree of conservation means that they can be trivially aligned to each other to study differences. But they also contain “hypervariable” regions that made it possible to distinguish different species at extremely high resolution, even using relatively slow computers and unsophisticated analytical tools. In addition, modern phylogeny mostly struggles with inconsistencies in classical methods that are due to unaccounted features (such as lateral gene transfer, which invalidates the typical assumption of a strict tree structure). Early studies ignored these inconsistencies (or didn’t even notice them, due to the scarcity of data).

But since you talk about correlative vs causative data, it’s important to note that this fundamentally hasn’t changed: from a very high-level perspective, new evidence is either compatible with existing theories, or isn’t. Strictly speaking, evidence never demonstrates causation — it can’t. But sometimes there are few viable alternative models, so the available evidence trivially allows discarding all but one or two models. This gets harder the more nuanced your models are, and this is the natural progression we have in any scientific endeavour.