What I'm going to say is completely my opinion, and I'm not accusing him of anything.
That being said, when I was watching the 10-second snippet of CPH on 48 Hours last night, I couldn't help but notice that his body language and behavior seemed odd. Now, I have to acknowledge that this was just a tiny snippet of footage that was taken of him, and I couldn't hear what he was saying or what was being asked of him. However, his body language is very weird IMO. He looks like he's talking to the media, then appears to me as if he realizes that he's either saying too much or talking to people who suspect him of something so he starts to turn his back and walk away. For whatever reason, he suddenly turns around and starts talking again. To be completely fair, I have no idea what the media were asking him, but based on his body language, it seemed to me as if his ego got in the way at the end and he had to turn around and say something to the media even though his first instinct (based on his turning around to go back into his house) was to walk away. Did anyone know what he was saying, or what was being said to him? His behavior looked impulsive and erratic (in my opinion) in that clip.
How about the emotional difference between the various news clips:
1. at his doorway - he looks winded and shocked and how he "can't believe it's even happening"
2. walking shot - excited and smiling by the cat and mouse game he is playing with the news (and the news is playing with him
3. semi-casual in the car - while wife is driving, notice how he touches face while answering questions, then tries to fix hair, then finally awkwardly closes his lips over his teeth in a self conscious gesture. (pants on fire)
4. on his steps with wife - in sunglasses, shook up and exhausted from "the tough couple of days" they have had because of this.
Why the sever range of emotions? In all of the clips Brewer is in, he seems to be the same stern, semi-douche, long island guy, an average New Yorker

Brewer doesn't seem to be enjoying any part of this investigation, or getting overly anxious about any part of it.
The range of post-crime behaviors usually include flight (check), participating in the investigation(check), fabricating an alibi(check, check) purpose in avoiding apprehension(check), enjoyment with the continuation of the fantasy (clip 2.)
Post-crime behavior often places the murderer at greater risk of apprehension (phone calls) but they seek the excitement of staying involved with the murder and continuing their fantasy (power).