Unlike our "friends" here at this board, I don't get to pretend this didn't happen. It did asnd I don't have a physical explaination for it.
No surprise to me some people believe in ghosts, or prehaps KNOW they exist would be a better way of putting it.
Why would any of us say it didn't happen?
I'd suggest that it wasn't a ghost, that your brother hallucinated Pete, but I wouldn't claim that the door didn't slam.
The human mind tries to identify patterns all the time, including patterns that aren't there. Just the other day while checking my mail, I could have sworn I saw a man in a striped shirt out of the corner of my eye. I could even give a basic description - somewhat heavyset, dark hair, caucasian, around 6' tall. Of course, when I looked
directly where I thought I saw him, there was only a plant, the fence around the apartment complex's tennis court, and beyond that a stairwell. There was no man - my brain simply assembled half-glanced images and interpreted an image that I would "expect."
Memory bias will by now have colored the experience for you, but I would hazard to guess that the car was parked on uneven ground such that the door closed itself, or there was a slight breeze that you simply didn't notice, or any number of other things that could cause a car door to close seemingly by itself. The remainder of your story is false pattern recognition, faulty memory (since there is a rather porous barrier in the human mind between "memory" and "fantasy"), and in the case of your brother, likely alcohol.
These are all far more mundane than a ghost slamming a door. Given the copious amounts of evidence we have for these mundane explanations (we have ample evidence that alcohol affects perception, that even a sober mind will identify patterns that don't exist, and that human memory is highly unreliable) and the utter lack of evidence that "ghosts" exist, the mundane explanation is far more likely.