I've found NPR to be pretty good at that. It's particularly apparent when it comes to Trump's lies about the 2020 election; they are consistent about pointing out when claims have been conclusively disproven, and often use the word "lie".
That said, I agree with Berliner's fundamental point; I've noticed an increasing slant in the stories NPR emphasizes. It's not that their reporting is unfair, but their choice of what to cover aligns pretty closely with the positions of the progressive left.