This shouldn't be the dawn of mistrust. Anyone who trusted the government was being, at the very least, gullible.
This is the surprise development of the information age... It was long thought that more information would give people a basis to make better decisions. The truth turned out to be that more information gave people more opportunity to discover facts that align with their beliefs. People trust data that says what they already think, they distrust data that says otherwise. It's always been that way.
The end result is that the trustworthiness of data is irrelevant in the public sphere. Regular people are simply discussing their opinion and hiding that opinion behind a "fact" they discovered.
Among experts in a field, data trustworthiness is important. However, experts are much better at validating data than the general public, so this usually isn't a problem.