Are they people you played with or jsut totally random? If you played with them then that's why; you can check your list of recently played with people (though it doesn't always keep up with every game). I don't understand why people send random invites, but you'll get them even if you don't play online. Some people are just desperate for friends I guess .
People on PSN are nicer from what iv'e seen I think its just less hardcore on PSN then people on XBOX LIVE I know it sounds like it shouldn't matter but I think people are more hardcore on XBOX LIVE so people on PSN seem nicer so you will get invites and friend adds.