IMO it’s not that blue check equals credibility, but rather it equals that you are who you say you are. This is a good thing particularly when it comes to public figures/officials — not for their sake, mind you, but for the sake of other people who may see a tweet from them. If the checkmark is there, then it’s them. If not, then it’s an impersonator. Right now it’s difficult to tell.

Tl;dr: it doesn’t make what they say real, it just makes them real.