That's a great way to lose any remaining confidence the population might have on the establishment. It is also probably unethical so I doubt any doctor would go with it.
It's a perfectly valid concern, but I don't think it needs to turn out the way your fear.
How about we try this: when reporting "facts", how about we try noting that there is uncertainty involved? I know the average Joe and Jane public aren't intellectuals, and it is often how stupid people can be, but on the other hand I think it is also fair to say that we underestimate people.
I think we should at least consider trying this (noting uncertainty in reporting) - it's times like this where we need more ideas and more thinking, not less.