Birth trauma can. An illness that causes swelling of the brain tissue can. Congenital issues can. Also, the medical condition may have not been correctly stated.
If mother was in rehab, sounds like Dad may have found baby more than he could handle. If baby tends to be sickly and fussy...maybe it just got to him that night.
That's something I find interesting...who takes a little baby out for a late-night walk in just a diaper? Interesting that he would phrase it that way. In a diaper. Late at night. I suspect something happen late at night, when baby was just in a diaper.