Simply getting computers to understand the statements is one of the holy grails of AI research; let alone determining if they are true.
Look into the fields of epistemology and the philosophy of science, in particular the works of Karl Popper such as The Logic of Scientific Discovery. The "truth" has always been an elusive concept. Outside the realm of mathematics, it's rather difficult to objectively prove most things "true".
That, in essence, is how we got here. There are plenty of loud, vocal defenders of "truth" out there, it's just that the loudest and most vocal of them define "truth" to mean "what our side believes".
The public at large has never been particularly well connected to truth. One difference now is that, in the past, the public at least respected and trusted scientists, academics, etc. Nowadays they're scorned.
How did we get to the state where the "truth" is such an elusive concept?
Is it so hard to determine whether basic statements are true or false? And to build larger, higher constructs out of those building blocks? That's basically what science has been and is.
It seems comically easy to identify fake news in most cases. Was this inauguration crowd larger than that one? That's a simple question to answer.