Hi Duchess - I think that the person on LinkedIn who posted that is confusing Wordpress.com's service with the millions of people who host their blogs there.......So whatever infringement has occurred is (I'm fairly certain) the fault of a single blogger, not WordPress.com.
To a large extent, WordPress.com does NOT moderate or control what content people who host their blogs with them post to their site - could you imagine if they did? People would complain about censorship and lack of free speech. It really isn't their job to be the "blog police". Imagine for a moment that the person who is complaining about copyright infringement isn't being truthful (I'm not doubting them, just posing a hypothetical example).....who is to say who is telling the truth? Should WordPress take down content and then find out that they shouldn't have? With millions (and that's not an exaggeration) of blogs hosted there, that would be such a monumentally full-time job that they would not be able to offer hosting for free.
However, I have heard that they will remove blogs for reasons such as illegal activity, hate mongering, or pornography. But those are pretty much black and white cases - no gray area - whereas a claim about copyright infringement is very, very, gray.