Nothing is purely true or false because everything falls on a continuum. Words can be strictly true but the sentiment can be false or vice versa.
So, a better system is one that attempts to trace back to the source and then you let the reader decide if it's true. Lots of things happen along the way until a news story gets to you.
Even direct access to the POTUS twitter account isn't the original source, he's just reciting something he heard. Until there is a technological system that quickly and immediately traces news stories back to the source we will all just continue to be stuck in our own confirmation biases.
News outlets protect their sources? Fine. Then the endpoint is that news source. I can then use analytics to discern how true that source has proven to be in the past and/or if the person saying it is typically left/right etc.
Based on data you can decide what to believe.
I'd also like to see some data on why the POTUS may be lying and not just the fact that he is lying. Sometimes its ego but other times its a red herring.
I like John Oliver (in doses) but after watching a few shows it's clear that his show is full of cognitive biases. It is impossible that he doesn't know that he's cutting corners at a minimum.
It got me thinking after his show on Apple and encryption. It was pretty clear that in that show he definitely took some creative license. After I thought about it, it makes sense; his whole show is about how ridiculous something is and not to provide both sides of a story.
Here's how you know the media is biased. When was the last time you turned on MSNBC and heard them say anything positive at all about the POTUS?
Even by accident he must have done something they would normally consider good.
You will lie to yourself (cognitive bias). the media lies in a number of ways, politicians lie in many different ways for different reasons and all of that comes to you by way of massive corporations who, well, you get my point.
Forget trying to find the truth. Focus on the source of the story then tear apart that source with data and analytics until you can reach some kind of consensus about the degree of truth you are hearing.