It might not be the best way, but it does seem plenty trendy.
Also, assuming a more 'official' response is in the works, a tweet is still faster so both are probably a decent idea during a time-sensitive event like bad publicity.
Maybe it's just because I don't use Twitter frequently, but an instance like this seems to highlight how ridiculous restricting yourself to 140 characters can be.
You have something important to say, and you're forced to drop pronouns and abbreviate words and break your message into several pieces. Your response to the world reads like a rushed text I'd get from my little sister.
To me, it just makes the whole thing feel somewhat petty.
Musk can control who sees his tweets, he can't control who prints his press release.
Putting the tweets out there ahead of time also changes the conversation's point-of-view. Now the public will demand answers from the NYT along with Musk while everyone waits for the data. Hell, he doesn't even need to publish the data for a while. Everyone can sit back and watch what the NYT does next.
Also, assuming a more 'official' response is in the works, a tweet is still faster so both are probably a decent idea during a time-sensitive event like bad publicity.