It's not immediately possible, but of course, as more information comes to light, you can verify of falsify it. So please show an example, from the last year, from the New York Times, where they published something from an anonymous source that was later disproven[1].
Here, I'll start with something that was proven to be right: Flynn's phone call with the ambassador was reported (with anonymous sources, on Jan 12th, and confirmed by the president's spokesman the next day: https://www.nytimes.com/interactive/2017/02/14/us/politics/f...
[1] Because I've learnt to qualify everything: This may actually happen on occasion, but I'd expect the journalist in question to acknowledge it, give an account of their relationship with the source, and what steps they are taking to avoid a repetition.