This is true. Absolutely true. They DO look. It's the first thing they do when your resume with your name on it hits their desks. They Google search you, they stalk your social media accounts, etc. They even run a credit check on your ass.
That's why I'm mcblink on the forums, and my actual name isn't used. You can't Google me. I've tried. You can find my family, my brother, my cousin, my cousin's kids, etc...but not me. I have no social media presence. (I have a unique enough surname that anyone else who shares it with me outside of Holland is a direct relative of mine)
Not entirely sure that it's always worked for me though. I have been looked at a little bit oddly in the past when employers can't find anything on me. It's abnormal in today's world.
Frankly, it's none of their business, as long as people show up and do their jobs, nothing in their private lives should matter to employers. Unfortunately, everyone just publishes everything about their private lives for the world to see, with little to no actual thought about what they are potentially doing to themselves or their futures.