First of all let me state that I am NOT a random kid just saying stuff. I'm 36 years old and have a Masters Degree in Information Technology. I don't just put out RANDOM information WITHOUT knowing what I am talking about. At a particular level, YES the publishers do host their own servers, BUT they ALSO tie into the larger Playstation Network. If they didn't then how do you explain this....
http://blogs.zdnet.com/gadgetreviews/?p=12734
Also here is information on how PSN works.
http://www.gamespot.com/news/6145981.html