I called her out from a distance when she was talking to her boss. But she didn`t respond.- This is correct but I personally would just say called her, and leave off the out word. But both ways are correct... Trolls like to call out everything on the Internet deliberately. We can say it`s the price of free speech.

Your examples are of 'calling out', but not 'being called out'. I'll explain the other meaning of 'call out' In the game hide and seek, if I "call you out", I reveal you, and you lose. Keep that in mind. Maybe I know Jessica didn't actually write the big report at work, it was someone else. If I tell everyone publicly the truth, you could also say, "I called out Jessica for not writing the report." Very embarressing for Jessica. She 'lost face' (another fun expression). In this case to be 'called out' doesn't mean someone actually yelled, "Jessica!!", it means the truth was revealed in a detrimental sort of way.