Hm. I've heard the exact opposite e.g. if you want to keep yourself accountable about doing something then you should tell everyone you know that you're doing it.
I think that only works if you tell people that will hold you accountable, like if you tell your spouse that you'll mow the lawn, they'll hold you to it. If you're posting "I'm going to lose weight this year!" on social media, people probably won't hold you accountable and you'll still be glad that you collected a bunch of likes and thumbsups without having to accomplish anything.