alt Hacker NewsNo health claim is ever proven. Even with overwhelming evidence for a claim we can't really say it's proven. At best we can say we have very high confidence, supported by a lot of data.
Further, what exactly are we supposed to believe? Should we read the NY Times or Nature and just accept that what gets published there is the absolute truth? As we know, many paradigms have been overturned over the years- sometimes requiring heroic efforts to change the status quo. Many of the health claims about cholesterol, fat intake, and other diet/nutrition have turned out to be less important that originally believed.
There are a few exceptions and even then I wouldn't call them "proof". For example, smoking causes cancer- we have enough evidence to safely conclude actual causality (multiple replicated double-blind experiments).
As a complete non-expert, as far as I can tell, the only true agreement out there is that certain very specific substances are bad for you if you consume them too often. That's tobacco, alcohol, painkillers...and that's about it for consensus ones, with alcohol having wiggle room among the public thanks to some poor studies.
Just about every other piece of nutrition advice out there can easily be categorized as controversial. Not in the sense that one side is obviously stupid or malicious, but in the sense that both sides earnestly think they are right.