The problem here is not divulging info about yourself, its not being able to say no to work. I will happily draw a line where my responsiblities end and if anybody asks me to go over that I will ask for a role review. Too many people get walked over at work, stand up for yourself and say no!
I don't think I disagree with that at all.
Still, I do think there's merit in keeping your personal life to yourself and not telling your coworkers more than they need to know. I'm not saying you should be stoic or a dick or anything; by all means engage in conversations and be nice. I'm just saying that it's important to have boundaries.
I tend to be someone who overshares a lot (hence my enormous word count on Hacker News), so I just try and keep this in mind.