Thank you for your input. I also do not know of any serious physicist who asserted that causality had been finally and definitively solved by SR; from what I was taught, it was as I said more a widespread idea that the majority of the educated shared, rather than one person's assertion.

Indeed, Hume's insight is more of a philosophical problem than a mathematical one. Hume showed that empiricism alone could never determine causality. Einstein's STR showed that causality can be determined empirically when aided by maths, a tool of the empiricist. It can be argued that STR does not definitively prove causality itself (perhaps very rightly so - again, I am not aware), however the salient point is that STR gave rise to the conception that Hume's insight had finally been resolved. To be clear, in order to resolve Hume's insight one only needed to demonstrate that through empiricism it is possible to establish causality.