There are four scenes explicitly filmed like celebrity events we are familiar with.
- Criminals leading a police chase on the Interstate in a white bronco.
- Hancock giving his penitence press conference before going into prison.
- Mary having a sunglasses-barely-disguising her breakdown on public streets.
- Ray giving a knowledgeless press conference about Hancock's medical emergency.
They're interesting in how resonant they are with our own guilty experience of getting news about Hollywood, but do they add anything to the film?
Well for one, they come off as pretty pathetic and our protagonists at their worst. Hancock's apology does not come off as genuine or well received (we'll contrast the two apologies in the movie in a later post), Mary is becoming detached from the narrative reality of the rest of the cast, and Ray knows nothing about what's happening to his friend.
So there's this sense of celebrity-treatment as like kryptonite (which itself has always been a metaphor for cynicism as the poison to Superman's symbol of hope), where it takes these characters we've been getting a human portrait of, and puts them through the grinder.
It also communicates to us the obvious fact that "The brief glimpse you get through these sorts of encounters never tells you all you need to know about these people."
One could go into territory of "celebrities are our modern day gods", since we see diagetic gods getting the celebrity treatment. But nothing else in the film backs that up - Hancock and Mary don't feed off the power of fame, other more famous people do not exhibit any superpowers, etc.
These tentpole scenes do help with the overall camerawork of this being a very close shot film, with some use of shaking cameras and a lot of intimate, claustrophobic shots in various high pressure scenes. This sort of faux-realism is a good way not of making it "seem real" but giving the feeling of what it's like to be there. We know the plot details of what's happening pretty easily, but we can see why it still feels so confusing in the moment. (Again, the spaghetti dinner scene is just great.)
 To a lesser degree there's also the Nancy Grace style CNN shows attacking him, and the radio call-in show where callers give their populist opinion about Hancock. But both of these are pretty common fare for action movies lately, and not really experimental in any sense. Though you may notice how the one caller who defends Hancock on the radio backs it up with noting how hot he is. This continues the theme started in the deleted sex scene whereby Hancock's few fans sexualize and objectify him, not really helping with his position as a degraded object in society.