I think what is implied is that they feel they can say whatever they want without thinking about the consequences.

This topic has recently become the subject of much discussion here in Norway, as recent events have brought more attention to the anonymous racist comments (and harassment) that are quite often found on public forums (such newspaper websites, etc.) There are some who claim that expecting people to sign their real names to their comments would raise the level of discourse, as people would have to take some responsibility for their speech.