I think that is why we are going to see a lot of his dead body, just like Joffrey and others. They want to emphasis it.
Research says people read headlines, not actual articles. Hence the headlines they produce.
How does it lower integrity? They want to keep a plot point hidden. Since when did lying about plot in a work of fiction become a problem? How else do you keep a surprise? On another note, it might be annoying, but Jon is dead. I think we all believe that. Now he won't stay that way, but they aren't lying about him being dead.
I actually have had that situation. My mother and brother have asked me about what happens in the story, as they haven't read the books and I have. Long phone conversations. Most of the time I tell them to just keep watching, but when it comes to "deaths" I tell them everyone is dead. I told them Sandor and Jon are dead. That Bran and Rickon were dead. I totally lied to them about it because death is different on GoT then other things. The way they kill people makes it a different dynamic.
As to why they do not go with staying silence. Because of what happened with Ned and the Red Wedding, they have had a certain response. Because of that, saying anything else with Jon would give up the ghost. Just like GRRM did when asked the reporter if they really thought Jon was dead. All the death has been building to this very moment. The moment when the hero does come back. The one where the fans finally get what they want. It is actually a rather power concept, especially on this show. It is exactly why they are doing this.
