Quick internet search didn't find much on his mile time, but he did do an interview where he talks about his dad being the 5th fastest 600 yard runner in the world in 1946. If his dad had that kind of ability then I don't doubt that he could run a 4:25 mile.
Heres the link to the interview
http://tengerresearch.com/learn/interviews/neildtyson_text.htm
It reminds me of my father, in fact I carry this example with me to this day. My father is 5’10”, lean and muscular, as opposed to bulky and muscular, a cross between a rock climber and a gymnast. He was in junior high school. He’s there on the line as you line up for gym class and the gym instructor is describing what kind of body types are suitable for different activities in the track and field. That’s kind of what makes track and field interesting because you can have different kinds of talent sets that reveal themselves in different events. So he said publicly in front of all the other students, “Take Cyril Tyson’s body for example, that would not make a good running body. He’s not built for running.” And my father said, “Nobody’s going to tell me what I can’t do.” So he took up running just because the guy said this. In 1946 (my father) had the 5th fastest time in the world for the 600-yard run. 5th fastest time in the world! So if you want to talk about resolve, he did that just out of spite!